Numerical Mathematics and Advanced Applications

The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) is a series of conferences held every two years to provide a forum for discussion on recent aspects of numerical mathematics and their applications. The ?rst ENUMATH conference was held in Paris (1995), and the series continued by the one in Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), and Santiago de Compostela (2005). This volume contains a selection of invited plenary lectures, papers presented in minisymposia, and contributed papers of ENUMATH 2007, held in Graz, Austria, September 10-14, 2007. We are happy that so many people have shown their interest in this conference. In addition to the ten invited presentations and the public lecture, we had more than 240 talks in nine minisymposia and ?fty four sessions of contributed talks, and about 316 participants from all over the world, specially from Europe. A total of 98 contributions appear in these proceedings. Topics include theoretical aspects of new numerical techniques and algorithms, as well as to applications in engineering and science. The book will be useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scienti?c computing and their applications. We would like to thank all the participants for the attendance and for their va- ablecontributionsanddiscussionsduringtheconference.Specialthanksgothe m- isymposium organizers, who made a large contribution to the conference, the chair persons, and all speakers.

InhaltsangabePlenary Lectures.- The Worst Scenario Method: A Red Thread Running Through Various Approaches to Problems with Uncertain Input Data.- Boundary and Finite Element Domain Decomposition Methods.- Discontinuous Galerkin Elements for Reissner-Mindlin Plates.- Contributed Lectures.- Functional Type A Posteriori Error Estimates for Maxwell's Equations.- Space-Time Adaption for Advection-Diffusion-Reaction Problems on Anisotropic Meshes.- A Posteriori Error Analysis for Kirchhoff Plate Elements.- Adaptive Finite Element Simulation of Relaxed Models for Liquid-Solid Phase Transition.- A Numerical Study of the Interaction of Blood Flow and Drug Release from Cardiovascular Stents.- Numerical Modelling of Epidermal Wound Healing.- Model of Multiple Lexicographical Programming Applied in Cervical Cancer Screening.- A Finite Element Model for Bone Ingrowth into a Prosthesis.- Space and Time Adaptive Calculation of Transient 3D Magnetic Fields.- A Boundary Integral Formulation for Nonlocal Electrostatics.- Efficient Solution of Algebraic Bernoulli Equations Using ?-Matrix Arithmetic.- A Purely Algebraic Approach to Preconditioning Based on Hierarchical LU Factorizations.- Additive Schwarz Preconditioners for Degenerate Problems with Isotropic Coefficients.- Performance Analysis of Parallel Algebraic Preconditioners for Solving the RANS Equations Using Fluctuation Splitting Schemes.- On Least-Squares Approximate Inverse-Based Preconditioners.- On the Construction of Stable B-Spline Wavelet Bases.- The Performance of a Multigrid Algorithm for the Acoustic Single Layer Equation.- Constraints Coefficients in hp-FEM.- A Boundary Element Algorithm for the Dirichlet Eigenvalue Problem of the Laplace Operator.- On Efficient Solution of Linear Systems Arising in hp-FEM.- Coupling Two Scalar Conservation Laws via Dafermos' Self-Similar Regularization.- A Sharp Interface and Fully Conservative Scheme for Computing Nonclassical Shocks.- A Numerical Descent Method for an Inverse Problem of a Scalar Conservation Law Modelling Sedimentation.- PSI Solution of Convection-Diffusion Equations with Data in L1.- High Order Two Dimensional Numerical Schemes for the Coupling of Transport Equations and Shallow Water Equations.- Well-Balanced High-Order MUSTA Schemes for Non-Conservative Hyperbolic Systems.- Local Time Stepping for Implicit-Explicit Methods on Time Varying Grids.- A 'TVD-like' Scheme for Conservation Laws with Source Terms.- Application of the WAF Method to Shallow Water Equations with Pollutant and Non-Constant Bottom.- A Third Order Method for Convection-Diffusion Equations with a Delay Term.- A Third Order WLSQR Scheme on Unstructured Meshes with Curvilinear Boundaries.- On the Choice of Parameters in Stabilization Methods for Convection-Diffusion Equations.- On Path-Conservative Numerical Schemes for Hyperbolic Systems of Balance Laws.- An Augmented DG Scheme for Porous Media Equations.- A Remark to the DGFEM for Nonlinear Convection-Diffusion Problems Applied on Nonconforming Meshes.- BDF-DGFE Method for the Compressible Navier-Stokes Equations.- Discontinuous Galerkin Method for the Numerical Solution of Inviscid and Viscous Compressible Flow.- Numerical Integration in the Discontinuous Galerkin Method for Nonlinear Convection-Diffusion Problems in 3D.- Implicit-Explicit Runge-Kutta Discontinuous Galerkin Finite Element Method for Convection-Diffusion Problems.- A Domain Decomposition Method Derived from the Primal Hybrid Formulation for 2nd Order Elliptic Problems.- A Posteriori Error Analysis of Penalty Domain Decomposition Methods for Linear Elliptic Problems.- BETI-DP Methods in Unbounded Domains.- Domain Decomposition and Model Reduction of Systems with Local Nonlinearities.- An Adaptive Discontinuous Galerkin Scheme for Second Order Problems with an Interface.- Abstract Sensitivity Analysis for Nonlinear Equations and Applications.- Multiscale Analysis for Jump Processes in Finance.- A Hybrid Numerical Scheme for Aerosol Dynamics.- Numer