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Advanced Finite Element Methods with Applications

Selected Papers from the 30th Chemnitz Finite Element Symposium 2017

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  • © 2019

Overview

Editors:
  1. Thomas Apel

    1. Institut für Mathematik & Computergestützte Simulation, Universität der Bundeswehr München, Neubiberg, Germany

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  2. Ulrich Langer

    1. Institute for Computational Mathematics, Johannes Kepler University Linz, Linz, Austria

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  3. Arnd Meyer

    1. Fakultät für Mathematik, TU Chemnitz, Chemnitz, Germany

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  4. Olaf Steinbach

    1. Institut für Angewandte Mathematik, Technische Universität Graz, Graz, Austria

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  • Features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium
  • The Symposium itself already has a 40-year tradition
  • Offers readers insights into the latest results

Part of the book series: Lecture Notes in Computational Science and Engineering (LNCSE, volume 128)

Included in the following conference series:

Conference proceedings info: FEM 2017.

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xxii
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  2. Superconvergent Graded Meshes for an Elliptic Dirichlet Control Problem

    • Thomas Apel, Mariano Mateos, Johannes Pfefferer, Arnd Rösch
    Pages 1-16

  3. Explicit and Implicit Reconstructions of the Potential in Dual Mixed hp-Finite Element Methods

    • Lothar Banz, Jan Petsche, Andreas Schröder
    Pages 17-40

  4. Two Stabilized Three-Field Formulations for the Biharmonic Problem

    • Lothar Banz, Jan Petsche, Andreas Schröder
    Pages 41-55

  5. Analysis of the hp-Version of a First Order System Least Squares Method for the Helmholtz Equation

    • Maximilian Bernkopf, Jens Markus Melenk
    Pages 57-84

  6. Numerical Study of Goal-Oriented Error Control for Stabilized Finite Element Methods

    • Marius Paul Bruchhäuser, Kristina Schwegler, Markus Bause
    Pages 85-106

  7. Uniform Exponential Stability of Galerkin Approximations for a Damped Wave System

    • Herbert Egger, Thomas Kugler
    Pages 107-129

  8. Adaptive Algorithm Based on Functional-Type A Posteriori Error Estimate for Reissner-Mindlin Plates

    • Maxim Frolov, Olga Chistiakova
    Pages 131-141

  9. Wavelet Boundary Element Methods: Adaptivity and Goal-Oriented Error Estimation

    • Helmut Harbrecht, Manuela Moor
    Pages 143-164

  10. Comparison Analysis of Two Numerical Methods for Fractional Diffusion Problems Based on the Best Rational Approximations of t γ on [0, 1]

    • Stanislav Harizanov, Raytcho Lazarov, Svetozar Margenov, Pencho Marinov, Joseph Pasciak
    Pages 165-185

  11. A Three-Level Extension of the GDSW Overlapping Schwarz Preconditioner in Two Dimensions

    • Alexander Heinlein, Axel Klawonn, Oliver Rheinbach, Friederike Röver
    Pages 187-204

  12. A Parallel Multigrid Solver for Multi-Patch Isogeometric Analysis

    • Christoph Hofer, Stefan Takacs
    Pages 205-219

  13. On a Renewed Approach to A Posteriori Error Bounds for Approximate Solutions of Reaction-Diffusion Equations

    • Vadim G. Korneev
    Pages 221-245

  14. Space-Time Finite Element Methods for Parabolic Evolution Problems with Variable Coefficients

    • Ulrich Langer, Martin Neumüller, Andreas Schafelner
    Pages 247-275

  15. ACA Improvement by Surface Segmentation

    • Sergej Rjasanow, Steffen Weißer
    Pages 277-295

  16. First Order Error Correction for Trimmed Quadrature in Isogeometric Analysis

    • Felix Scholz, Angelos Mantzaflaris, Bert Jüttler
    Pages 297-321

  17. A Space–Time Finite Element Method for the Linear Bidomain Equations

    • Olaf Steinbach, Huidong Yang
    Pages 323-339

  18. A Stabilized Space–Time Finite Element Method for the Wave Equation

    • Olaf Steinbach, Marco Zank
    Pages 341-370

  19. An Optimal Order CG-DG Space-Time Discretization Method for Parabolic Problems

    • Igor Voulis
    Pages 371-386

  20. A Framework for Efficient Hierarchic Plate and Shell Elements

    • Michael Weise
    Pages 387-413
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Keywords

About this book

Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.



Editors and Affiliations

  • Institut für Mathematik & Computergestützte Simulation, Universität der Bundeswehr München, Neubiberg, Germany

    Thomas Apel

  • Institute for Computational Mathematics, Johannes Kepler University Linz, Linz, Austria

    Ulrich Langer

  • Fakultät für Mathematik, TU Chemnitz, Chemnitz, Germany

    Arnd Meyer

  • Institut für Angewandte Mathematik, Technische Universität Graz, Graz, Austria

    Olaf Steinbach

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