Numerical Mathematics and Advanced Applications: Proceedings of ENUMATH 2003 the 5th European Conference on Numerical Mathematics and Advanced Applications Prague, August 2003

872 Pages·2004·39.011 MB·English

by  Alfredo Bermúdez, Rodolfo Rodríguez, Pilar Salgado (auth.), Miloslav Feistauer, Vít Dolejší, Petr Knobloch, Karel Najzar (eds.)

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, [email protected]
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
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Preface
These proceedings collect the major part of the lectures given at ENU
MATH2003, the European Conference on Numerical Mathematics and Ad
vanced Applications, held in Prague, Czech Republic, from 18 August to 22
August, 2003.
The importance of numerical and computational mathematics and sci
entific computing is permanently growing. There is an increasing number of
different research areas, where numerical simulation is necessary. Let us men
tion fluid dynamics, continuum mechanics, electromagnetism, phase transi
tion, 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 fo
rum for discussion of current topics of numerical mathematics. They seek to
convene leading experts and young scientists with special emphasis on con
tributions 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 Fac
ulty, 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 contem
porary 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 Jin
dfich 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 com
mittee for the cooperation in the organization of the conference. Finally, we
are gratefully indebted to O. Ulrych for the TEX editing and the prepara
tion 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 obtain
ing 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 Element
Finite 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 Time
Dependent 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