Numerical Mathematics and Advanced Applications - Proceedings of ENUMATH 2005 the 6th European Conference on Numerical Mathematics and Advanced Applications, Santiago de Compostela, Spain, July 2005

Preface

Contents

PLENARY LECTURES

Compatible Discretizations in Two Dimensions

1 Introduction

2 Construction of the dual complex

3 Applications

References

Finite Element Approximation of the Three Field Formulation of the Elasticity Problem Using Stabilization

1 Introduction

2 Problem statement and Galerkin finite element discretization

3 Finite element approximation using subscales

4 Numerical analysis of the original formulation

5 A modified stabilized problem

6 Concluding remarks

References

Convergence of Adaptive Wavelet Methods for Goal– Oriented Error Estimation*

1 Introduction

2 Goal–oriented error estimation

3 Adaptive error estimation

4 Numerical experiments

References

Quadratic Programming and Scalable Algorithms for Variational Inequalities

1 Introduction

2 Bound constrained problems

3 Bound and equality constrained problems

4 Model problem

5 FETI and total FETI domain decomposition

6 FETI–DP domain decomposition and discretization

7 Numerical scalability

8 Numerical experiments

9 Comments and conclusions

Acknowledgements

References

Discontinuous Galerkin Methods for Friedrichs’ Systems

1 Introduction

2 Friedrichs’ systems

3 Design and analysis of DG methods

4 DG approximation of two-field Friedrichs’ systems

5 Examples

6 Concluding remarks

References

Highly Oscillatory Quadrature: The Story so Far

1 The challenge of high oscillation

2 Asymptotic expansion in the absence of critical points

3 Asymptotic, filon and levin methods

4 Critical points

5 Conclusions and pointers for further research

References

The 3D Inverse Electromagnetic Scattering Problem for a Coated Dielectric

1 Introduction

2 Formulation of the direct and inverse scattering problem

3 Analysis of the inverse problem

4 Numerical example

5 Conclusion

Acknowledgment

References

Functional Approach to Locally Based A Posteriori Error Estimates for Elliptic and Parabolic Problems

1 Introduction

2 Functional a posteriori estimates for elliptic problems

3 Functional a posteriori estimates for a model evolutionary problem

References

Finite Element Approximation of 2D Parabolic Optimal Design Problems

1 Introduction

2 Preliminaries

3 Preliminaries on the convergence of the numerical scheme

4 Convergence of discrete optimal shapes

5 Gradient calculations: A numerical approach

6 Conclusions

Acknowledgements

References

CONTRIBUTED LECTURES

3D Free Surface Flows Simulations Using a Multilayer Saint- Venant Model. Comparisons with Navier- Stokes Solutions

1 Introduction

2 Navier-Stokes equations and hydrostatic approximation

3 A Multilayer saint-venant system

4 Numerical method

5 Numerical results

References

Some Well-Balanced Shallow Water-Sediment Transport Models

1 Sediment transport model

2 Finite volume method for non conservative hyperbolic systems

3 High order schemes based on state reconstruction

4 Numerical test: comparison with an analytical solution

References

Highly Accurate Conservative Finite Difference Schemes and Adaptive Mesh Refinement Techniques for Hyperbolic Systems of Conservation Laws*

1 Introduction

2 Finite-difference Shu-Osher schemes

3 Adaptive mesh refinement for Shu-Osher schemes

4 Numerical examples

5 Conclusions

References

Finite Volume Solvers for the Shallow Water Equations Using Matrix Radial Basis Function Reconstruction

1 Finite volume methods for shallow water models

2 Matrix valued Radial Basis Functions for vector field reconstruction

3 Applications to environmental modelling

References

On Numerical Schemes for a Hierarchy of Kinetic Equations

1 Introduction

2 Hexagonal kinetic models

3 Hexagonal hierarchy

4 Coupling of two kinetic models

References

Computational Aspects of the Mesh Adaptation for the Time Marching Procedure

1 Euler equations

2 Adaptive algorithm

3 Anisotropic mesh adaptation

4 Geometric mass conservation law

5 Numerical example

Acknowledgement

References

On the Use of Slope Limiters for the Design of Recovery Based Error Indicators

1 Introduction

2 A posteriori error indication

3 Limited gradient averaging

4 Limited gradient reconstruction

5 Adaptation strategy

6 Numerical examples

7 Conclusions

References

On a Superconvergence Result for Mixed Approximation of Eigenvalue Problems

1 Introduction

2 Statement of the problem and its discretization

3 Main results

4 Numerical results

References

Comparative Study of the a Posteriori Error Estimators for the Stokes Problem

1 Introduction

2 The stokes problem and its approximation

3 Estimation of the deviation from the exact solution

4 Numerical experiments

References

Error Control for Discretizations of Electromagnetic- Mechanical Multifield Problem

1 Introduction

2 Electromagnetic forming

3 Error control for coupled and mixed problems

References

A Safeguarded Zienkiewicz-Zhu Estimator

1 Introduction

2 Error estimator and theoretical results

3 Numerical results

References

Some Remarks on a Model for the Atmospheric Pressure in Ocean Dynamics

1 Introduction

2 Modelling of non-hydrostatic free-surface flows

3 A linearised model for the free surface equation

References

Computational Time Improvement for Some Shallow Water Finite Volume Models Applying Parallelization and Optimized Small Matrix Computations.

1 Introduction

2 Equations

3 Numerical scheme

4 Parallel SIMD implementation

References

Discretization Error Estimates for an Optimal Control Problem in a Nonconvex Domain

1 Introduction

2 Theory

3 Numerical results

References

A Posteriori Estimates for Cost Functionals of Optimal Control Problems

1 Introduction

2 Majorants for the cost functional

3 Properties of majorants

4 Practical implementation

5 Numerical experiments

References

Optimization of a Duality Method for the Compressible Reynolds Equation

1 The mathematical model

2 Numerical solution

3 Optimization of the duality algorithm

4 Numerical examples

5 Conclusions

Aknowledgments

References

Time-Space & Space-Time Elements for Unsteady Advection- Dominated Problems

1 Introduction

2 Stabilization techniques for the stationary problem

3 Stabilized methods for the non-stationary problem

4 Numerical Experiments

Acknowledgements

References

On Discontinuity–Capturing Methods for Convection– Diffusion Equations

1 Introduction

2 Galerkin’s finite element discretization

3 The SUPG method

4 Methods diminishing spurious oscillations in layers

5 Conclusions

Acknowledgements

References

Algebraic Flux Correction for Finite Element Approximation of Transport Equations

1 Introduction

2 Flux decomposition

3 Algebraic flux correction

4 Numerical example

5 Conclusions

References

A Parallel Multiparametric Gauss-Seidel Method*

1 Introduction

2 The local modified extrapolated Gauss-Seidel ( LMEGS) method

3 The eigenvalue relationship

4 Determination of good values

5 Numerical results and conclusions

Acknowledgement

References

A Numerical Scheme for the Micro Scale Dissolution and Precipitation in Porous Media

1 Introduction

2 The numerical scheme

3 A fixed point iteration

4 A numerical example

Acknowledgment

References

Discrete Kinetic Methods for a Degenerate Parabolic Equation in Dimension Two.

1 Introduction

2 Kinetic models

3 The numerical schemes

4 Numerical experiments

References

Anisotropic Doubly Nonlinear Degenerate Parabolic Equations

1 Introduction

2 Entropy solution

3 Renormalized entropy solution

Acknowledgement

References

A Multiresolution Method for the Simulation of Sedimentation- Consolidation Processes

1 Introduction

2 The multiresolution scheme

3 Sedimentation-consolidation processes

4 Numerical results

Acknowledgements

References

Diffusive Relaxation Limit for Hyperbolic Systems

1 Introduction

2 BGK approximation of strongly parabolic systems

3 One–dimensional semilinear model in viscoelasticity

4 Multidimensional viscoelasticity and modulated energy

References

Parallel Algorithms for Nonlinear Diffusion by Using Relaxation Approximation

1 Relaxation approximation of nonlinear diffusion

2 The numerical scheme

3 Numerical results

4 Concluding remarks

References

On a Degenerated Parabolic-Hyperbolic Problem Arising From Stratigraphy

1 Introduction and presentation of the model

2 A locally hyperbolic behaviour

3 Definition of a solution and existence results for a discretized problem

4 Some numerical illustrations

5 Conclusion and open problems

References

Schwarz Domain Decomposition Preconditioners for Interior Penalty Approximations of Elliptic Problems

1 Introduction

2 Discontinuous Galerkin methods for elliptic problems

3 Non-overlapping Schwarz methods

4 Convergence analysis

5 Numerical results

References

Higher Order Semi-Implicit Discontinuous Galerkin Finite Element Schemes for Nonlinear Convection- Diffusion Problems*

1 Introduction

2 Scalar equation

3 Numerical results

4 Conclusion

References

On Some Aspects of the Discontinuous Galerkin Method*

1 Continuous problem

2 Discretization of the problem

3 Error estimates

4 Application of the DGFEM to compressible flow with a wide range of mach numbers

5 Conclusion

References

Mixed Discontinuous Galerkin Methods with Minimal Stabilization

1 DG methods

2 Minimal stabilization

3 Numerical results

References

Discontinuous Galerkin Finite Element Method for a Fourth- Order Nonlinear Elliptic Equation Related to the Two- Dimensional Navier– Stokes Equations

1 Introduction

2 Mathematical formulation

3 DGFEM for a 4th-order advective PDE

4 Numerical results

References

Fourier Method with Nitsche-Mortaring for the Poisson Equation in 3D

1 Introduction

2 Fourier decomposition and mortaring in 2D

3 Fourier-nitsche-finite-element approximation in 3D

References

Substructuring Preconditioners for the Bidomain Extracellular Potential Problem

1 Introduction

2 Mortar method

3 Substructuring preconditioners

References

A Face Penalty Method for the Three Fields Stokes Equation Arising from Oldroyd- B Viscoelastic Flows

1 Introduction

2 A finite element formulation

3 The inf-sup condition

4 A priori error estimates

5 A stable iterative algorithm

6 Preliminary numerical results

References

Anisotropic H1-Stable Projections on Quadrilateral Meshes

1 Introduction

2 Anisotropic H1-stable projectors

3 General result

References

Continuous Interior Penalty hp-Finite Element Methods for Transport Operators

1 Introduction

2 Continuous interior penalty finite element methods

3 Technical results

4 Convergence analysis

5 Numerical results

References

A Nonconforming Finite Element Method with Face Penalty for Advection– Diffusion Equations

1 Introduction

2 The nonconforming finite element scheme with face penalty

3 A posteriori error estimates

4 Numerical results

Acknowledgment

References

Efficient Multigrid and Data Structures for Edge- Oriented FEM Stabilization

1 Introduction

2 Sparsity of the matrix

3 Local pressure Schur complement approach

4 Numerical example

References

Adaptive Methods for Dynamical Micromagnetics

1 Introduction

2 Numerical methods

3 Adaptive algorithm

4 Numerical experiment

References

Stability for Walls in Ferromagnetic Nanowire

1 Model for ferromagnetic nanowires

2 Landau-Lifschitz Equation in the mobile frame

3 A new system of coordinates

4 Estimates for the perturbations

References

Continuous Galerkin Methods for Solving Maxwell Equations in 3D Geometries

1 Introduction and notations

2 Variational formulations and discretization

3 Numerical results and conclusion

References

On the Use of the Gautschi-Type Exponential Integrator for Wave Equations

1 Introduction

2 Sine–Gordon equation

3 Discretisation

4 The Gautschi-type exponential integrator

5 Numerical example

References

Positivity of Exponential Multistep Methods

1 Introduction

2 Analytical framework

3 Exponential multistep methods

4 Positivity and order barrier

References

Stability Results and Algorithmic Strategies for the Finite Element Approach to the Immersed Boundary Method

1 Introduction

2 The finite element immersed boundary method

3 Time discretization by finite differences

4 Stability analysis by energy estimates

5 Numerical results

6 Conclusions

References

A Comparison of Enthalpy and Temperature Methods for Melting Problems on Composite Domains

1 Introduction

2 Problem description

3 Numerical methods

4 Numerical experiments

5 Conclusions

References

Qualitative Properties of a Numerical Scheme for the Heat Equation

1 Introduction

2 Proof of the results

Acknowledgements

References

Modeling Radiation and Moisture Content in Fire Spread

1 Introduction

2 Physical model

3 Governing equations

4 Numerical method

5 Numerical results

Acknowledgement

References

Fast Multipole Method for Solving the Radiosity Equation

1 Introduction

2 Radiosity equation and numerical solution

3 FMM and kernel expansion

4 A new fast method

5 Numerical results

6 Conclusion

References

Numerical Modelling of Kinetic Equations

1 Introduction

2 Asymptotic method

3 Numerical examples

References

On a Subclass of H¨ older Continuous Functions with Applications to Signal Processing

1 Introduction

2 H¨ older continuous spaces

3 Generalized Harten’s Subcell resolution technique

4 Numerical experiments

Acknowledgments

References

Modelisation and Simulation of Static Grain Deep- Bed Drying

1 Introduction

2 Models

3 The numerical schemes

4 Numerical experiments and comparisons

References

Hybrid Godunov-Glimm Method for a Nonconservative Hyperbolic System with Kinetic Relations

1 Introduction

2 The PDE model and main properties

3 Godunov-Glimm Hybrid method

4 The nonlinear projection

References

Cell-Average Multiwavelets Based on Hermite Interpolation*

1 Introduction

2 Harten’s framework for multiresolution analysis

3 Vector multiresolution analysis for cell-averaged data

4 Numerical experiments

References

On a General Definition of the Godunov Method for Nonconservative Hyperbolic Systems. Application to Linear Balance Laws

1 Introduction

2 Choice of paths

3 Godunov’s method

4 Application to linear balance laws

Acknowledgements

References

Sequential Flux-Corrected Remapping for ALE Methods

1 Introduction

2 Sequential FCR method

3 Numerical examples

Acknowledgments

References

Orthogonal hp-FEM for Elliptic Problems Based on a Non- Affine Concept

1 Introduction and historical remarks

2 Preliminaries

3 Numerical example

4 Construction of basis functions

5 Numerical example continued

Acknowledgment

References

On Some Aspects of the hp-FEM for Time- Harmonic Maxwell’s Equations

1 Introduction

2 Formulation of the problem

3 Shape functions

4 Numerical experiments

5 Conclusion and outlook

Acknowledgment

References

Numerical Simulation of Phase-Transition Front Propagation in Thermoelastic Solids

1 Introduction

2 Formulation of the problem

3 Conservative wave propagation algorithm

4 Contact quantities and numerical fluxes

5 Conclusions

Acknowledgment

References

The Level Set Method for Solid-Solid Phase Transformations

1 Introduction

2 The physical problem

3 The computational method

4 Numerical results

5 Conclusions

References

A Non-Monotone Fast Marching Scheme for a Hamilton- Jacobi Equation Modelling Dislocation Dynamics*

1 Introduction

2 The FMM algorithm for unsigned velocity

3 Numerical tests

Acknowledgments

References

A Time–Adaptive Semi–Lagrangian Approximation to Mean Curvature Motion

1 Introduction

2 General requirements on the adaptation strategy for geometric equations

3 A strategy based on local truncation error

4 Numerical tests

References

Heterogeneous Multiscale Methods with Quadrilateral Finite Elements

1 Introduction

2 HMM with quadrilaterals finite elements

3 Error analysis

4 Numerical experiments

Acknowledgment

References

Stabilizing the P1/P0 Element for the Stokes Problem via Multiscale Enrichment

1 Introduction

2 The model problem and the general framework

3 Application to the

pair

4 Numerical validations

References

Adaptive Multiresolution Methods for the Simulation of Shocks/ Shear Layer Interaction in Confined Flows

1 Introduction

2 Numerical results

3 Conclusion and perspectives

References

Local Projection Stabilization for the Stokes System on Anisotropic Quadrilateral Meshes

1 Introduction

2 Local projection stabilization on isotropic meshes

3 Anisotropic affine linear meshes

4 Local projection stabilization on anisotropic meshes

References

An Interior Penalty Variational Multiscale Method for High Reynolds Number Flows

1 Introduction

2 The equations of incompressible flow

3 Separation of scales and stabilized finite element methods

4 A posteriori error estimation

5 A numerical result

References

Variational Multiscale Large Eddy Simulation of Turbulent Flows Using a Two- Grid Finite Element or Finite Volume Method

1 Introduction

2 Multiscale formulation

3 Numerical results for turbulent flow in a diffuser

4 Conclusions

Acknowledgements

References

Issues for a Mathematical Definition of LES

1 Introduction

2 Suitable approximations

3 Review of existing pre–LES–models

4 Discretization

References

Stabilized FEM with Anisotropic Mesh Refinement for the Oseen Problem

1 Introduction

2 Stabilized FEM for linearized Navier-Stokes problem

3 Stability and convergence on hybrid meshes

4 Error estimates and design of stabilization parameters

5 Application to channel flow

Acknowledgment

References

Semi-Implicit Multiresolution for Multiphase Flows

1 Introduction

2 Semi implicit scheme on uniform grid

3 Multiscale analysis of the explicit-implicit scheme

References

Numerical Simulation of Vortex-Dipole Wall Interactions Using an Adaptive Wavelet Discretization with Volume Penalisation

1 Introduction

2 Adaptive wavelet discretization with volume penalisation

3 Vortex-dipole wall interactions

4 Conclusions

Acknowledgements

References

Inviscid Flow on Moving Grids with Multiscale Space and Time Adaptivity

1 Introduction

2 The ALE formulation of the Euler equations

3 Finite volume discretization

4 Adaptive multiscale method

5 Numerical results

References

A Relaxation Method for a Two Phase Flow with Surface Tension

1 Introduction

2 Numerical approximation

3 Relaxation method for the simplified model with surface tension forces

4 Numerical results

5 Conclusion

References

Extension of Interface Coupling to General Lagrangian Systems

1 Introduction

2 Coupling two p- systems

3 Coupling two Euler systems in Lagrangian coordinates

4 Coupling Lagrangian systems of different dimensions

5 Conclusion

References

A Numerical Scheme for the Modeling of Condensation and Flash Vaporization in Compressible Multi- Phase Flows

1 Introduction

2 The thermodynamics of phase transition

3 The Riemann problem with phase transition at equilibrium

4 The Riemann problem with out of equilibrium EOS

5 Numerical scheme

6 Numerical results

7 Conclusions

Acknowledgments

References

An Adaptive Operator Splitting of Higher Order for the Navier- Stokes Equations

1 Introduction

2 The Taylor based gradient recovery technique

3 The stabilized base splitting

4 The multi-grid postprocessing

5 Numerical results

6 Conclusions

Acknowledgment

References

The POD Technique for Computing Bifurcation Diagrams: A Comparison among Different Models in Fluids

1 Introduction

2 The POD technique

3 Description of the examples

4 Computation of the bifurcation diagrams of the example models

5 Conclusions

Acknowledgement

References

Filtering of Singularities in a Marangoni Convection Problem

1 Introduction

2 Formulation of the problem

3 Basic state

4 Linear stability

5 Conclusions

Acknowledgments

References

On Application of Stabilized Higher Order Finite Element Method on Unsteady Incompressible Flow Problems

1 Mathematical model

2 Time-spatial discretization

3 Numerical solution and results

References

Numerical Simulation of Coupled Fluid-Solid Systems by Fictitious Boundary and Grid Deformation Methods

1 Introduction

2 Grid deformation method

3 Numerical solution of the fluid-solid system

4 Verification of the numerical techniques

5 Conclusions

References

An Iterative Method for Solving Non-Linear Hydromagnetic Equations

1 Introduction. Statement of the problem

2 An iterative method for the magnetostatic system

3 Finite element discretization

4 Computational tests

References

Mathematical and Numerical Analysis of a Class of Non- linear Elliptic Equations in the Two Dimensional Case

1 Introduction

2 Statement of the main result

3 Proof of theorem 1

4 Numerical method

References

A s-step Variant of the Double Orthogonal Series Algorithm

1 Introduction

2 The algorithm of the Double Orthogonal Series

3 s-Step methods

4 The s-step variant of the double orthogonal series

5 Numerical results

6 Conclusions

Acknowledgment

References

Linear Equations in Quaternions

1 Basic properties and definitions for quaternions

2 Linear equations in quaternions

Acknowledgment

References

Computing the Analytic Singular Value Decomposition via a Pathfollowing

1 Introduction

2 Formulation of the problem

3 Solving defining equations

4 Experiments

5 Conclusions

Acknowledgments

References

A Jacobi-Davidson Method for Computing Partial Generalized Real Schur Forms

1 Introduction

2 The RJDQZ method for real matrix pencils

3 Numerical comparison

4 Conclusions

References

Pricing Multi-Asset Options with Sparse Grids and Fourth Order Finite Differences

1 Introduction

2 Model

3 Discretization

4 Sparse grid combination technique

5 Numerical results

6 Conclusions

References

A Third Order Linearly Implicit Fractional Step Method for Semilinear Parabolic Problems

1 Introduction

2 A new third order linearly implicit FSRK method

3 Numerical tests

References

Numerical Solution of Optimal Control Problems with Sparse SQP- Methods

1 Introduction

2 Optimal control problem

3 SQP-methods

4 Equality constrained quadratic subproblem

5 Approximation of the Hessian

6 Example

References

Semi-Deterministic Recursive Optimization Methods for Multichannel Optical Filters

1 Introduction

2 Global optimization methods

3 Application to multichannel optical filters design

4 Conclusions

References

A Multigrid Method for Coupled Optimal Topology and Shape Design in Nonlinear Magnetostatics*

1 Introduction

2 Topology optimization for magnetostatics

3 Sequential coupling of topology and shape optimization

4 Multilevel shape optimization

5 Numerical results

6 Conclusion

References

Nonsmooth Optimization of Eigenvalues in Topology Optimization

1 Introduction

2 Topology optimization and eigenproblems

3 Nonsmooth analysis

4 Numerical results

5 Conclusion

References

Derivative Free Optimization of Stirrer Configurations

1 Introduction

2 Flow solver and numerical optimization tool

3 Results

4 Conclusion

Acknowledgment

References

Mathematical Modelling and Numerical Optimization in the Process of River Pollution Control

1 Introduction

2 Mathematical formulation

3 Numerical solution

4 Numerical results

Acknowledgements

References

A Family of C0 Finite Elements for Kirchhoff Plates with Free Boundary Conditions

1 Introduction

2 Kirchhoff plate bending problem

3 Finite element formulation

4 A-priori error estimates

5 A-posteriori error estimates

6 Computational results

References

A Postprocessing Method for the MITC Plate Elements

1 Introduction

2 The Reissner–Mindlin plate model

3 MITC finite element methods

4 Superconvergence

5 Postprocessing method

6 Benchmark computations

References

A Uniformly Stable Finite Difference Space Semi- Discretization for the Internal Stabilization of the Plate Equation in a Square

1 Statement of the main result

2 Proof of Theorem 1

References

An e-Uniform Hybrid Scheme for Singularly Perturbed 1- D Reaction- Diffusion Problems

1 Introduction

2 The cubic spline-cum-finite difference scheme

3 Uniform convergence analysis on a Shishkin mesh

4 Numerical experiments

5 Conclusions

References

A Dynamic Frictional Contact Problem of a Viscoelastic Beam

1 Introduction

2 The variational formulation

3 Numerical approximation

4 Numerical results

Acknowledgements

References

Numerical Analysis of a Frictional Contact Problem for Viscoelastic Materials with Long- Term Memory

1 Introduction

2 The model and its well-posedness

3 Fully discrete approximation

4 Numerical simulations

Acknowledgments

References

A Suitable Numerical Algorithm for the Simulation of the Butt Curl Deformation of an Aluminium Slab

1 Introduction

2 Mathematical model

3 Weak formulation

4 Numerical solution

5 Numerical results

References

An Efficient Solution Algorithm for Elastoplasticity and its First Implementation Towards Uniform h- and p- Mesh Refinements

1 Introduction

2 The Model of Elastoplasticity

3 The algorithm

4 Numerical experiments

5 Conclusions and future work

Acknowledgment

References

A LDG-BEM Coupling for a Class of Nonlinear Exterior Transmission Problems

1 Introduction

2 An exterior transmission problem

3 LDG-BEM coupling

Acknowledgements

References

High Order Boundary Integral Methods for Maxwell’s Equations: Coupling of Microlocal Discretization and Fast Multipole Methods

1 Introduction

2 The integral equations of Despr ´ es (EID) and MLFMM

3 Finite elements of higher order and MLFMM

4 Microlocal discretization (MD) and MLFMM

5 Numerical results

6 Conclusion

References

Indirect Methods with Brakhage–Werner Potentials for Helmholtz Transmission Problems

1 Problem

2 Boundary integral formulation

3 Petrov–Galerkin methods

4 Numerical approximation in two dimensions

5 A numerical example

Acknowledgements

References

A FEM–BEM Formulation for a Time– Dependent Eddy Current Problem

1 Introduction

2 Model problem

3 Semi–discrete problem

References

Mixed Boundary Element–Finite Volume Methods for Thermohydrodynamic Lubrication Problems*

1 Introduction

2 Thermohydrodynamic mathematical model

3 Numerical solution of hydrodynamic and fluid thermal models

4 Numerical solution in the bush and the shaft

5 Numerical solution of the global problem

6 Extension to the evolution problem

References

Numerical Modelling for Leaching of Pesticides in Soils Modified by a Cationic Surfactant

1 Introduction

2 Laboratory experiments

3 Models describing leaching of solutes in soils

4 Numerical methods

5 Parameter adjustment

6 Examples

Acknowledgement

References

Formulation of Mixed-Hybrid FE Model of Flow in Fractured Porous Medium*

1 Rock Massif environment

2 Linear steady Darcy’s flow

3 Mathematical formulation of the problem

4 Mixed-hybrid formulation

5 Finite element approximation

6 Conclusions

References

Newton–Type Methods for the Mixed Finite Element Discretization of Some Degenerate Parabolic Equations

1 Introduction

2 The fully discrete problem

3 The Newton scheme

4 Conclusions

References

Domain Decomposition Methods for Wave Propagation in Heterogeneous Media

1 Formulation of the problem

2 Time discretization

3 Fully discrete scheme

4 Energy inequality

5 Numerical experiments

References

Galbrun’s Equation Solved by a First Order Characteristics Method

1 Galbrun’s equation

2 Characteristic curves

3 Numerical approximation

Acknowledgment

References

Open Subsystems of Conservative Systems

1 Overview

2 Open systems within conservative extensions

3 Discussion

References

Author Index