This volume on some recent aspects of finite element methods and their applications is dedicated to Ulrich Langer and Arnd Meyer on the occasion of their 60th birthdays in 2012. Their work combines the numerical analysis of finite element algorithms, their efficient implementation on state of the art hardware architectures, and the collaboration with engineers and practitioners. In this spirit, this volume contains contributions of former students and collaborators indicating the broad range of their interests in the theory and application of finite element methods.
Topics cover the analysis of domain decomposition and multilevel methods, including hp finite elements, hybrid discontinuous Galerkin methods, and the coupling of finite and boundary element methods; the efficient solution of eigenvalue problems related to partial differential equations with applications in electrical engineering and optics; and the solution of direct and inverse field problems in solid mechanics.
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From the Contents: A Brief History of the Parallel Dawn in Karl-Marx-Stadt/Chemnitz.- Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes.- Fast Domain Decomposition Algorithms for Elliptic Problems with Piecewise Variable Orthotropism.- Inexact Additive Schwarz Solvers for hp-FEM Discretizations in Three Dimensions.- A Rigorous Error Analysis of Coupled FEM-BEM Problems with Arbitrary Many Subdomain.- A Review of Anisotropic Refinement Methods for Triangular Meshes in FEM.- A Postprocessing Finite Element Strategy for Poisson’s Equation in Polygonal Domains: Computing the Stress Intensity Factors.
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