Numerical Mathematics and Advanced Applications

M.Feistauer • V. Dolejsi • P. Knobloch • K. Najzar

Editors

Numerical Mathematics and Advanced Applications

Proceedings of ENUMATH 2003 the 5th European Conference on Numerical Mathematics and Advanced Applications

Prague, August 2003

~ Springer

Editors

Miloslav Feistauer Vit Dolejsf Petr Knobloch Karel Najzar

Charles University Prague Facuhy of Mathematics and Physics Department of Numerical Mathematics Sokolovska 83, 186 75 Praha 8

Czech Republic

email: feist, dolejsi, knobloch, knaj@karlin.mff.cuni.cz

Library of Congress Control Number: 2004lO7015 Mathematics Subject Classification (2000): 65-XX, 74-XX, 76-XX, 78-XX

ISBN 978-3-642-62288-5 ISBN 978-3-642-18775-9 (eBook) DOI 10.1007/978-3-642-18775-9 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concemed, specifically the rights oftranslation, reprinting, reuse ofillustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law ofSeptember 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law.

© Springer-Verlag Berlin Heidelberg 2004 Originally published by Springer-Verlag Berlin Heidelberg New Y 0I:k in 2004 Softcover reprint of the hardcover lst edition 2004

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Preface

These proceedings collect the major part of the lectures given at ENU­MATH2003, the European Conference on Numerical Mathematics and Ad­vanced Applications, held in Prague, Czech Republic, from 18 August to 22 August, 2003.

The importance of numerical and computational mathematics and sci­entific computing is permanently growing. There is an increasing number of different research areas, where numerical simulation is necessary. Let us men­tion fluid dynamics, continuum mechanics, electromagnetism, phase transi­tion, cosmology, medicine, economics, finance, etc. The success of applications of numerical methods is conditioned by changing its basic instruments and looking for new appropriate techniques adapted to new problems as well as new computer architectures.

The ENUMATH conferences were established in order to provide a fo­rum for discussion of current topics of numerical mathematics. They seek to convene leading experts and young scientists with special emphasis on con­tributions from Europe. Recent results and new trends are discussed in the analysis of numerical algorithms as well as in their applications to challenging scientific and industrial problems.

The first ENUMATH conference was organized in Paris in 1995, then the series continued by the conferences in Heidelberg 1997, Jyvaskyla 1999 and Ischia Porto 2001. It was a great pleasure and honour for the Czech numerical community that it was decided at Ischia Porto to organize the ENUMATH2003 in Prague. It was the first time when this conference crossed the former Iron Courtain and was organized in a postsocialist country.

The ENUMATH2003 was organized by the Faculty of Mathematics and Physics of the Charles University in cooperation with the Department of Mathematics of the Institute of Chemical Technology in Prague. The Charles University, the oldest university in the Middle Europe, was founded in 1348. In the middle ages, mathematics was studied in Prague at the Artistic Fac­ulty, later at the Philosophical Faculty and in the 20th century it belonged to the Faculty of Natural Sciences till 1952, when the Faculty of Mathematics and Physics was founded. As follows from historical sources, already in the 15th century the students of the Charles University had the opportunity to be trained in "Computational Mathematics". Kfisfan from Prachatice, who

vi Preface

is in the Czech history well-known as a Church reformer (he was a friend of the famous reformer Jan Hus), or a personal doctor of medicine of the Czech and German-Roman King Wenceslas IV, was a professor of astronomy and mathematics at the Charles University. He wrote lecture notes with the title "Algoritmus Prosaicus", where he describes among other approximate methods for the realization of various mathematical operations. The contem­porary Czech school of numerical and applied mathematics was born much later in the second part of the 20th century. It is connected mainly with the names of Ivo Babuska, who can be considered as a father of the Czech numerical mathematics, Karel Rektorys, Milan Prager, Emil Vitasek, Milos Zlamal, Alexander Zenisek, Ivan Hlavacek, a famous specialist in PDE's Jin­dfich Necas (who influenced a number of Czech numerical analysts) and Jan Polasek (who founded the Prague school of CFD).

These proceedings contain a selection of invited plenary lectures, papers presented in minisymposia and works communicated within the sessions. All contributions of these proceedings have been reviewed by members of the Scientific Committee. At this occasion we want to thank the members of the Program Committee (F. Brezzi, M. Feistauer, R. Glowinski, R. Jeltsch, Yu. Kuznetsov, J. Periaux, R. Rannacher) and the members of the Scientific Committee (0. Axelsson, C. Bernardi, C. Canuto, M. Griebel, R. Hoppe, G. Kobelkov, M. Krizek, P. Neittaanmiiki, O. Pironneau, A. Quarteroni, C. Schwab, E. Stili, W. Wendland) for their scientific support. We are grateful to the plenary speakers R. Blaheta, A. Bermudez, T. Gallouet, J. Haslinger, R. Hiptmair, T. Hughes, J. Rappaz, A. Russo, A. Tveito and V. Schulz for coming to Prague and richly contributing to the success of the conference.

We are very much obliged to A. Klic, the head of the Department of Mathematics of the Institute of Chemical Technology, and our colleagues J. Felcman, J. Segethova and E. Plandorova from the local organizing com­mittee for the cooperation in the organization of the conference. Finally, we are gratefully indebted to O. Ulrych for the TEX editing and the prepara­tion of the camera-ready manuscript of the proceedings. Lastly, we thank all participants for coming and animating the meeting.

We believe that this volume will be an invaluable instrument for obtain­ing an overview of the latest and newest results and aspects of numerical mathematics and scientific computing and their applications.

M. Feistauer V. DolejSi

P. Knobloch K. Najzar

editors

Table of Contents

Part I Plenary Lectures

Numerical Analysis of Finite Element Methods for Eddy Current Problems. Applications to Electrode Simulation Alfredo Bermudez, Rodolfo Rodriguez, Pilar Salgado. . . . . . . . . . . . . . . . . 3

Space Decomposition Preconditioners and Parallel Solvers Radim Blaheta. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20

Boundary Conditions for Hyperbolic Equations or Systems Thierry Gallouet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39

Fictitious Domain Methods in Shape Optimization with Applications in Free-Boundary Problems Jaroslav Haslinger, Tomas Kozubek, Karl Kunisch, Gunter Peichl . . . .. 56

Part II Contributed Papers

Domain Decomposition Method for a Class of Non-Linear Elliptic Equation with Arbitrary Growth Nonlinearity and Data Measure Nour Eddine Alaa, Jean Rodolphe Roche .......................... 79

Variants of Relaxation Schemes and the Lattice Boltzmann Model Relaxation Systems Mapundi Kondwani Banda ...................................... 89

A Time Semi-Implicit Relaxation Scheme for Two-Phase Flows in Pipelines Michael Baudin, Frederic Coquel, Quang-Huy Tran . ................. 102

Computational Study of Field Scale BTEX Transport and Biodegradation in the Subsurface Markus Bause .................................................. 112

viii Table of Contents

A Two-Level Stabilization Scheme for the N avier-Stokes Equations Roland Becker, Malte Braack . .................................... 123

A Posteriori Error Estimates for Parameter Identification Roland Becker, Boris Vexler . ..................................... 131

On a Phase-Field Model with Advection Michal Benes . .................................................. 141

Fast Evaluation of Eddy Current Integral Operators Steffen Borm ................................................... 151

Adaptive Computation of Reactive Flows with Local Mesh Refinement and Model Adaptation Malte Braack, Alexandre Ern . .................................... 159

An Alternative to the Least-Squares Mixed Finite Element Method for Elliptic Problems Jan Brandts, Yanping Chen . ..................................... 169

Limit Analysis Method in Electrostatics Igor A. Brigadnov . .............................................. 176

Finite Element Mesh Adjusted to Singularities Applied to Axisymmetric and Plane Flow Pavel Burda, Jaroslav Novotny, Bedfich Soused{k, Jakub S{stek ....... 186

The Edge Stabilization Method for Finite Elements in CFD Erik Burman, Peter Hansbo ...................................... 196

Analysis and Computation of Dendritic Growth in Binary Alloys Using a Phase-Field Model Eric Burman, Marco Picasso, Jacques Rappaz ...................... 204

Discontinuous Galerkin Methods for Timoshenko Beams Fatila Celiker, Bernardo Cockburn, Sukru Giizey, Ramdev Kanapady, Sew-Chew Soon, Henrik K. Stolarski, Kummar Tamma .............. 221

Numerical Algorithms for Solving Elliptic-Parabolic Problems Raimondas Ciegis .............................................. 232

Stochastic Relaxation of Variational Integrals with N on-attainable Infima Dennis D. Cox, Petr Kloucek, Daniel R. Reynolds, Pavel Sol{n ....... 239

Table of Contents ix

A Pressure-Weighted Upwind Scheme in Unstructured Finite-Element Grids Masond Darbandi, Kinmars Mazaheri-Body, Shidvash Vakilipour . ..... 250

Discontinuous Galerkin Finite Element Method for the Numerical Solution of Viscous Compressible Flows Vit Dolejif{ ..................................................... 260

A Finite Volume Scheme on General Meshes for the Steady N avier-Stokes Equations in Two Space Dimensions Robert Eymard, Raphaie Herbin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

Existence and Uniqueness of a Weak Solution to a Stratigraphic Model Robert Eymard, Thierry Gallouei, Veron'iqne Gervais, Roland Masson. 278

Combined Nonconforming/Mixed-hybrid Finite Element­Finite Volume Scheme for Degenerate Parabolic Problems Robert Eymard, Danielle Hilhorst, Martin Vohmlzk ..... ............. 288

Discrete Maximum Principle for Galerkin Finite Element Solutions to Parabolic Problems on Rectangular Meshes Istvan Famg6, R6bert Horvath, Sergey Korotov ..................... 298

Cubature-Differences Method for Singular Integro-differential Equations Alexander I. Fedotov ............................................ 308

Nonconforming Discretization Techniques for Overlapping Domain Decompositions Bernd Flem'isch, Michael Mair, Barbam Wahlm71th . ................. 316

On the Use of Implicit Updates in Minimum Curvature Multi-step Quasi-Newton Methods John A. Ford, Issam A. Moghmbi . ................................ 326

A Boundary Movement Identification Method for a Parabolic Partial Differential Equation Tom P. Fredman . ............................................... 336

On Computational Properties of a Posteriori Error Estimates Based upon the Method of Duality Error Majorants Maxim Frolov, Pekka Neittaanmiib, Sergey Repin . .................. 346

Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods Rao Garimella, Milan K nchai'zk, Mikhail Shashkov ................. 358

x Table of Contents

Mimetic Finite Difference Methods for Diffusion Equations on Unstructured Triangular Grid Victor Ganzha, Richard Liska, Mikhail Shashkov, Christoph Zenger 368

On Computational Glaciology: FE-Simulation of Ice Sheet Dynamics Gunter Godert, Franz- Theo Suttmeier ............................. 378

Nonreflecting Boundary Conditions for Multiple Domain Wave Scattering in Unbounded Media Marcus J. Grote, Christoph Kirsch, Patrick Meury .................. 391

On the Choice of the Regularization Parameter in the Case of the Approximately Given Noise Level of Data Uno Hiimarik, Toomas Raus . ..................................... 400

Adaptive Discontinuous Galerkin Finite Element Methods with Interior Penalty for the Compressible Navier-Stokes Equations Ral! Hartmann, Paul Houston . ................................... 410

On a Novel Technique for Parallel Unstructured Mesh Generation in 3D Jan Haskovec, Pavel Bolin . ...................................... 420

Adaptive Finite Element Methods for Turbulent Flow Johan Hoffman, Claes Johnson . .................................. 430

Numerical Solution of a Nonlinear Evolution Equation Describing Amorphous Surface Growth of Thin Films Ronald H. W. Hoppe, Eva Nash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440

Constrained Mountain Pass Algorithm for the Numerical Solution of Semilinear Elliptic Problems Jif{ Horak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449

Optimal Shape Design of Diesel Intake Ports with Evolutionary Algorithm Andras Horvath, Zoltan Horvath . ................................. 459

Numerical Simulation of Compressible Fluids with Moving Boundaries: An Effective Method with Applications Zoltan Horvath, Andras Horvath . ................................. 471

Discontinuous Galerkin Methods for the Time-Harmonic Maxwell Equations Paul Houston, Ilaria Perugia, Anna Schneebeli, Dominik Schotzau .... 483

Table of Contents xi

Mixed hp-Discontinuous Galerkin Finite Element Methods for the Stokes Problem in Polygons Paul Houston, Dominik Schotzau, Thomas P. Wihler ................ 493

A Postprocessing of Hopf Bifurcation Points Dasa Janovska, Vladimir Janovsky . ............................... 502

Givens' Reduction of Quaternion-Valued Matrices to Upper Hessenberg Form Drahoslava Janovska, Gerhard Opfer . ............................. 510

Model of Compressible Flow and Transport in a Time­Dependent Domain Pavel Jiranek, Jiri Maryska, Jan Sembera . ......................... 521

Numerical Study of Convection of Multi-Component Fluid in Porous Medium Olga Kantur, Vyacheslav Tsybulin ................................ 531

Multi-yield Elastoplastic Continuum-Modeling and Computations Johanna Kienesberger, Jan Valdman .............................. 539

Celebrating Fifty Years of David M. Young's Successive Overrelaxation Method David R. Kincaid ............................................... 549

On the Relational Database Style Parallel Numerical Programming Bela Kiss, Anna Krebsz ......................................... 559

A Dynamical System Describing Evolution of the Implicit Surfaces in Incompressible Viscous Liquids Petr Kloucek, Michel V. Romerio, Jennifer L. Wightman ............ 569

Discrete Maximum Principles in Finite Element Modelling Sergey Korotov, Michal Krizek . ................................... 580

A Posteriori Error Estimation in Terms of Linear Functionals for Boundary Value Problems of Elliptic Type Sergey Korotov, Pekka Neittaanmiiki, Sergey Repin . ................. 587

Numerical Solution of Flow in Backward Facing Step Karel Kozel, Petr Louda, Petr Svacek ............................. 596

Periodicity Properties of Solutions to a Hysteresis Model in Micromagnetics Marlin K ruzz'k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605

Xli Table of Contents

Mixed Finite Element Method on Polygonal and Polyhedral Meshes Yuri Kuznetsov, Sergey Repin .................................... 615

Semi-discrete Schemes for Hamilton-Jacobi Equations on Unstructured Grids Doron Levy, Suhas Nayak ........................................ 623

Numerical Simulation of Dislocation Dynamics Vojtech Minarik, Jan Kratochvzl, Karol Mikula, Michal Benes . ....... 631

Implicit FEM-FCT algorithm for compressible flows Matthias Moller, Dmitri Kuzmin, Stefan Turek . .................... 641

A Singular Limit Method for the Stefan Problems Hideki Murakawa, Tatsuyuki Nakaki . .............................. 651

Higher-Order Split-Step Schemes for the Generalized Nonlinear Schrodinger Equation Gulcin M. Muslu, Husnu A. Erbay ................................ 658

Numerical Methods and Simulation Techniques for Flow with Shear and Pressure Dependent Viscosity Abderrahim Ouazzi, Stefan Turek ................................. 668

Piecewise Polynomial Approximations for Linear Volterra Integro-Differential Equations with Nonsmooth Kernels Arvet Pedas .................................................... 677

On a Discontinuous Galerkin Method for Radiation-Diffusion Problems Ilaria Perugia, Dominik Schotzau, James Warsa .................... 687

Modeling of Multi-Phase Flows with a Level-Set Method Sander P. van der Pijl, A. Segal, C. Vuik .......................... 698

Numerical Modeling of Bypass Flow Vladimir Prokop, Karel Kozel . ................................... 708

A Posteriori Estimation of Dimension Reduction Errors Sergey Repin, Stefan Sauter, Anton Smolianski ..................... 716

Analysis of a Multi-NumericsjMulti-Physics Problem Beatrice Riviere ................................................ 726

The Discontinuous Galerkin Method for Singularly Perturbed Problems Hans-Gorg Roos, Helena Zarin ................................... 736

Table of Contents Xlll

A Finite-Volume Mass- and Vorticity-Conserving Shallow­Water Model using Penta-/Hexagonal Grids William Sawyer, Rolf leltsch ..................................... 746

Application of Parallel Computing Techniques for Problems of Degenerated Diffusion Milan Senkyr, liN Mikyska, Michal Benes . ........................ 756

The Finite Element Analysis of an Elliptic Problem with a Nonlinear Newton Boundary Condition Veronika SoboUkova ............................................. 766

Automatic Goal-Oriented hp-Adaptivity Without Error Estimates Pavel Solin, Leszek Demkowicz ................................... 775

A Compression Method for the Helmholtz Equation Mirjam Stolper, Sergej Rjasanow ................................. 786

Application of a Stabilized FEM to Problems of Aeroelasticity Petr Svacek, Miloslav Feistauer ................................... 796

A Numerical Approach to the Dynamical Behavior of Initiated Pulses in Some Nonlinear Diffusion Equations Kenji Tomoeda ................................................. 806

Fully Two-dimensional HLLEC Riemann Solver and Associated Difference Schemes Pavel Vachal, Richard Liska, Burton Wendroff ..................... 815

Deflation Accelerated Parallel Preconditioned Conjugate Gradient Method in Finite Element Problems Fred I. Vermolen, Kees Vuik, Guus Segal . ......................... 825

Advantages of Binomial Checkpointing for Memory-reduced Adjoint Calculations Andrea Walther, Andreas Griewank ............................... 834

An Efficient Multigrid FEM Solution Technique for Incompressible Flow with Moving Rigid Bodies Decheng Wan, Stefan Turek, Liudmila S. Rivkind ................... 844

Higher-Order FEM for a System of Nonlinear Parabolic PDE's in 2D with A-Posteriori Error Estimates Martin Zitka, Karel Segeth, Pavel Solin . ........................... 854