Numerical Mathematics and Advanced Applications

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.

I Plenary Lectures.- Numerical Analysis of Finite Element Methods for Eddy Current Problems. Applications to Electrode Simulation.- Space Decomposition Preconditioners and Parallel Solvers.- Boundary Conditions for Hyperbolic Equations or Systems.- Fictitious Domain Methods in Shape Optimization with Applications in Free-Boundary Problems.- II Contributed Papers.- Domain Decomposition Method for a Class of Non-Linear Elliptic Equation with Arbitrary Growth Nonlinearity and Data Measure.- Variants of Relaxation Schemes and the Lattice Boltzmann Model Relaxation Systems.- A Time Semi-Implicit Relaxation Scheme for Two-Phase Flows in Pipelines.- Computational Study of Field Scale BTEX Transport and Biodegradation in the Subsurface.- A Two-Level Stabilization Scheme for the Navier-Stokes Equations.- A Posteriori Error Estimates for Parameter Identification.- On a Phase-Field Model with Advection.- Fast Evaluation of Eddy Current Integral Operators.- Adaptive Computation of Reactive Flows with Local Mesh Refinement and Model Adaptation.- An Alternative to the Least-Squares Mixed Finite Element Method for Elliptic Problems.- Limit Analysis Method in Electrostatics.- Finite Element Mesh Adjusted to Singularities Applied to Axisymmetric and Plane Flow.- The Edge Stabilization Method for Finite Elements in CFD.- Analysis and Computation of Dendritic Growth in Binary Alloys Using a Phase-Field Model.- Discontinuous Galerkin Methods for Timoshenko Beams.- Numerical Algorithms for Solving Elliptic-Parabolic Problems.- Stochastic Relaxation of Variational Integrals with Non-attainable Infima.- A Pressure-Weighted Upwind Scheme in Unstructured Finite-Element Grids.- Discontinuous Galerkin Finite Element Method for the Numerical Solution of Viscous Compressible Flows.- A Finite Volume Scheme on General Meshes for the Steady Navier-Stokes Equations in Two Space Dimensions.- Existence and Uniqueness of a Weak Solution to a Stratigraphic Model.- Combined Nonconforming/Mixed-hybrid Finite Element-Finite Volume Scheme for Degenerate Parabolic Problems.- Discrete Maximum Principle for Galerkin Finite Element Solutions to Parabolic Problems on Rectangular Meshes.- Cubature-Differences Method for Singular Integro-differential Equations.- Nonconforming Discretization Techniques for Overlapping Domain Decompositions.- On the Use of Implicit Updates in Minimum Curvature Multi-step Quasi-Newton Methods.- A Boundary Movement Identification Method for a Parabolic Partial Differential Equation.- On Computational Properties of a Posteriori Error Estimates Based upon the Method of Duality Error Majorants.- Efficient Algorithm for Local-Bound-Preserving Remapping in ALE Methods.- Mimetic Finite Difference Methods for Diffusion Equations on Unstructured Triangular Grid.- On Computational Glaciology: FE-Simulation of Ice Sheet Dynamics.- Nonreflecting Boundary Conditions for Multiple Domain Wave Scattering in Unbounded Media.- On the Choice of the Regularization Parameter in the Case of the Approximately Given Noise Level of Data.- Adaptive Discontinuous Galerkin Finite Element Methods with Interior Penalty for the Compressible Navier-Stokes Equations.- On a Novel Technique for Parallel Unstructured Mesh Generation in 3D.- Adaptive Finite Element Methods for Turbulent Flow.- Numerical Solution of a Nonlinear Evolution Equation Describing Amorphous Surface Growth of Thin Films.- Constrained Mountain Pass Algorithm for the Numerical Solution of Semilinear Elliptic Problems.- Optimal Shape Design of Diesel Intake Ports with Evolutionary Algorithm.- Numerical Simulation of Compressible Fluids with Moving Boundaries: An Effective Method with Applications.- Discontinuous Galerkin Methods for the Time-Harmonic Maxwell Equations.- Mixed hp-Discontinuous Galerkin Finite Element Methods for the Stokes Problem in Polygons.- A Postprocessing of Hopf Bifurcation Points.- Givens’ Reduction of Quaternion-Valued Matrices to Upper Hessenberg Form.- Model of Compressible Flow and Transport in a Time-Dependent Domain.- Numerical Study of Convection of Multi-Component Fluid in Porous Medium.- Multi-yield Elastoplastic Continuum-Modeling and Computations.- Celebrating Fifty Years of David M. Young’s Successive Overrelaxation Method.- On the Relational Database Style Parallel Numerical Programming.- A Dynamical System Describing Evolution of the Implicit Surfaces in Incompressible Viscous Liquids.- Discrete Maximum Principles in Finite Element Modelling.- A Posteriori Error Estimation in Terms of Linear Functionals for Boundary Value Problems of Elliptic Type.- Numerical Solution of Flow in Backward Facing Step.- Periodicity Properties of Solutions to a Hysteresis Model in Micromagnetics.- Mixed Finite Element Method on Polygonal and Polyhedral Meshes.- Semi-discrete Schemes for Hamilton-Jacobi Equations on Unstructured Grids.- Numerical Simulation of Dislocation Dynamics.- Implicit FEM-FCT algorithm for compressible flows.- A Singular Limit Method for the Stefan Problems.- Higher-Order Split-Step Schemes for the Generalized Nonlinear Schrödinger Equation.- Numerical Methods and Simulation Techniques for Flow with Shear and Pressure Dependent Viscosity.- Piecewise Polynomial Approximations for Linear Volterra Integro-Differential Equations with Nonsmooth Kernels.- On a Discontinuous Galerkin Method for Radiation-Diffusion Problems.- Modeling of Multi-Phase Flows with a Level-Set Method.- Numerical Modeling of Bypass Flow.- A Posteriori Estimation of Dimension Reduction Errors.- Analysis of a Multi-Numerics/Multi-Physics Problem.- The Discontinuous Galerkin Method for Singularly Perturbed Problems.- A Finite-Volume Mass- and Vorticity-Conserving Shallow-Water Model using Penta-/Hexagonal Grids.- Application of Parallel Computing Techniques for Problems of Degenerated Diffusion.- The Finite Element Analysis of an Elliptic Problem with a Nonlinear Newton Boundary Condition.- Automatic Goal-Oriented hp-Adaptivity Without Error Estimates.- A Compression Method for the Helmholtz Equation.- Application of a Stabilized FEM to Problems of Aeroelasticity.- A Numerical Approach to the Dynamical Behavior of Initiated Pulses in Some Nonlinear Diffusion Equations.- Fully Two-dimensional HLLEC Riemann Solver and Associated Difference Schemes.- Deflation Accelerated Parallel Preconditioned Conjugate Gradient Method in Finite Element Problems.- Advantages of Binomial Checkpointing for Memory-reduced Adjoint Calculations.- An Efficient Multigrid FEM Solution Technique for Incompressible Flow with Moving Rigid Bodies.- Higher-Order FEM for a System of Nonlinear Parabolic PDE’s in 2D with A-Posteriori Error Estimates.