The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) is a series of meetings held every two years to provide a forum for discussion on recent aspects of numerical mathematics and their applications. These proceedings collect the major part of the lectures given at ENUMATH 2005, held in Santiago de Compostela, Spain, from July 18 to 22, 2005. Topics include applications such as fluid dynamics, electromagnetism, structural mechanics, interface problems, waves, finance, heat transfer, unbounded domains, numerical linear algebra, convection-diffusion, as well as methodologies such as a posteriori error estimates, discontinuous Galerkin methods, multiscale methods, optimization, etc.
This book collects the major part of the lectures given at ENUMATH 2005, the Sixth European Conference on Numerical Mathematics and Advanced Applications, that took place in Santiago de Compostela, Spain, from July 18 to 22, 2005. It contents text of invited speakers, and a selection of papers presented in minisymposia andInhalt
contributed sessions. Topics include applications such as atmosphere and ocean, water
pollution, electromagnetism, interface problems, waves, finance, heat transfer, unbounded domains, numerical linear algebra, convection-diffusion, fluid-structure, plates, solids, hyperbolic equations, multiphase flow, Navier-Stokes, singular perturbation problems, non linear PDE, control, parabolic equations, as well as methodologies such as a posteriori error estimates, discontinuous Galerkin methods, multiscale methods, optimization, adaptive methods, domain decomposition techniques, exponential integrators, hp-finite elements, level set methods, fractional step methods, penalty procedures, and finite volumes. The book gives an extensive overview of the most recent research in scientific computing, providing to the reader the latest developments concerning the mathematical issues and the applications of this active field of science.
PLENARY LECTURES.- Compatible Discretizations in Two Dimensions.- Finite Element Approximation of the Three Field Formulation of the Elasticity Problem Using Stabilization.- Convergence of Adaptive Wavelet Methods for Goal-Oriented Error Estimation.- Quadratic Programming and Scalable Algorithms for Variational Inequalities.- Discontinuous Galerkin Methods for Friedrichs' Systems.- Highly Oscillatory Quadrature: The Story so Far.- The 3D Inverse Electromagnetic Scattering Problem for a Coated Dielectric.- Functional Approach to Locally Based A Posteriori Error Estimates for Elliptic and Parabolic Problems.- Finite Element Approximation of 2D Parabolic Optimal Design Problems.- CONTRIBUTED LECTURES.- 3D Free Surface Flows Simulations Using a Multilayer Saint-Venant Model. Comparisons with Navier-Stokes Solutions.- Some Well-Balanced Shallow Water-Sediment Transport Models.- Highly Accurate Conservative Finite Difference Schemes and Adaptive Mesh Refinement Techniques for Hyperbolic Systems of Conservation Laws.- Finite Volume Solvers for the Shallow Water Equations Using Matrix Radial Basis Function Reconstruction.- CONTRIBUTED LECTURES.- On Numerical Schemes for a Hierarchy of Kinetic Equations.- Computational Aspects of the Mesh Adaptation for the Time Marching Procedure.- On the Use of Slope Limiters for the Design of Recovery Based Error Indicators.- CONTRIBUTED LECTURES.- On a Superconvergence Result for Mixed Approximation of Eigenvalue Problems.- Comparative Study of the a Posteriori Error Estimators for the Stokes Problem.- Error Control for Discretizations of Electromagnetic-Mechanical Multifield Problem.- A Safeguarded Zienkiewicz-Zhu Estimator.- CONTRIBUTED LECTURES.- Some Remarks on a Model for the Atmospheric Pressure in Ocean Dynamics.- Computational Time Improvement for Some Shallow Water Finite Volume Models Applying Parallelization and Optimized Small Matrix Computations..- CONTRIBUTED LECTURES.- Discretization Error Estimates for an Optimal Control Problem in a Nonconvex Domain.- A Posteriori Estimates for Cost Functionals of Optimal Control Problems.- CONTRIBUTED LECTURES.- Optimization of a Duality Method for the Compressible Reynolds Equation.- Time-Space & Space-Time Elements for Unsteady Advection-Dominated Problems.- On DiscontinuityCapturing Methods for ConvectionDiffusion Equations.- Algebraic Flux Correction for Finite Element Approximation of Transport Equations.- A Parallel Multiparametric Gauss-Seidel Method.- A Numerical Scheme for the Micro Scale Dissolution and Precipitation in Porous Media.- CONTRIBUTED LECTURES.- Discrete Kinetic Methods for a Degenerate Parabolic Equation in Dimension Two..- Anisotropic Doubly Nonlinear Degenerate Parabolic Equations.- A Multiresolution Method for the Simulation of Sedimentation-Consolidation Processes.- Diffusive Relaxation Limit for Hyperbolic Systems.- Parallel Algorithms for Nonlinear Diffusion by Using Relaxation Approximation.- On a Degenerated Parabolic-Hyperbolic Problem Arising From Stratigraphy.- CONTRIBUTED LECTURES.- Schwarz Domain Decomposition Preconditioners for Interior Penalty Approximations of Elliptic Problems.- Higher Order Semi-Implicit Discontinuous Galerkin Finite Element Schemes for Nonlinear Convection-Diffusion Problems.- On Some Aspects of the Discontinuous Galerkin Method.- Mixed Discontinuous Galerkin Methods with Minimal Stabilization.- Discontinuous Galerkin Finite Element Method for a Fourth-Order Nonlinear Elliptic Equation Related to the Two-Dimensional Navier-Stokes Equations.- CONTRIBUTED LECTURES.- Fourier Method with Nitsche-Mortaring for the Poisson Equation in 3D.- Substructuring Preconditioners for the Bidomain Extracellular Potential Problem.- CONTRIBUTED LECTURES.- A Face Penalty Method for the Three Fields Stokes Equation Arising from Oldroyd-B Viscoelastic Flows.- Anisotropic H 1-Stable Projections on Quadrilateral Meshes.- Continuous Interior Penalty hp-Finite Element Methods for Transport Operators.- A Nonconforming Finite Element Method with Face Penalty for AdvectionDiffusion Equations.- Efficient Multigrid and Data Structures for Edge-Oriented FEM Stabilization.- CONTRIBUTED LECTURES.- Adaptive Methods for Dynamical Micromagnetics.- Stability for Walls in Ferromagnetic Nanowire.- Continuous Galerkin Methods for Solving Maxwell Equations in 3D Geometries.- CONTRIBUTED LECTURES.- On the Use of the Gautschi-Type Exponential Integrator for Wave Equations.- Positivity of Exponential Multistep Methods.- CONTRIBUTED LECTURES.- Stability Results and Algorithmic Strategies for the Finite Element Approach to the Immersed Boundary Method.- CONTRIBUTED LECTURES.- A Comparison of Enthalpy and Temperature Methods for Melting Problems on Composite Domains.- Qualitative Properties of a Numerical Scheme for the Heat Equation.- Modeling Radiation and Moisture Content in Fire Spread.- Fast Multipole Method for Solving the Radiosity Equation.- Numerical Modelling of Kinetic Equations.- CONTRIBUTE...