Mathematical Aspects of Finite Elements in Partial Differential Equations
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Mathematical Aspects of Finite Elements in Partial Differential Equations

Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, April 1 – 3, 1974

  1. 430 pages
  2. English
  3. PDF
  4. Only available on web
eBook - PDF

Mathematical Aspects of Finite Elements in Partial Differential Equations

Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, April 1 – 3, 1974

Book details
Table of contents
Citations

About This Book

Mathematical Aspects of Finite Elements in Partial Differential Equations addresses the mathematical questions raised by the use of finite elements in the numerical solution of partial differential equations. This book covers a variety of topics, including finite element method, hyperbolic partial differential equation, and problems with interfaces. Organized into 13 chapters, this book begins with an overview of the class of finite element subspaces with numerical examples. This text then presents as models the Dirichlet problem for the potential and bipotential operator and discusses the question of non-conforming elements using the classical Ritz- and least-squares-method. Other chapters consider some error estimates for the Galerkin problem by such energy considerations. This book discusses as well the spatial discretization of problem and presents the Galerkin method for ordinary differential equations using polynomials of degree k. The final chapter deals with the continuous-time Galerkin method for the heat equation. This book is a valuable resource for mathematicians.

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Information

Publisher
Academic Press
Year
2014
ISBN
9781483268071
Topic
Mathematics
Subtopic
Mathematical Analysis
Index
Mathematics

Table of contents

  1. Front Cover
  2. Mathematical Aspects of Finite Elements in Partial Differential Equations
  3. Copyright Page
  4. Table of Contents
  5. Preface
  6. Chapter 1. Higher Order Local Accuracy by Averaging in the Finite Element Method
  7. Chapter 2. Convergence of Nonconforming Methods
  8. Chapter 3. Some Convergence Results for Galerkin Methods for Parabolic Boundary Value Problems
  9. Chapter 4. On a Finite Element Method for Solving the Neutron Transport Equation
  10. Chapter 5. A Mixed Finite Element Method for the Biharmonic Equation
  11. Chapter 6. A Dissipative Galerkin Method for the Numerical Solution of First Order Hyperbolic Equations
  12. Chapter 7. C1 Continuity via Constraints for 4th Order Problems
  13. Chapter 8. Finite Element and Finite Difference Methods for Hyperbolic Partial Differential Equations
  14. Chapter 9. Solution of Problems with Interfaces and Singularities
  15. Chapter 10. The Construction and Comparison of Finite Difference Analogs of Some Finite Element Schemes
  16. Chapter 11. L2 Error Estimates for Projection Methods for Parabolic Equations in Approximating Domains
  17. Chapter 12. An H' 1 -Galerkin Procedure for the Two-Point Boundary Value Problem
  18. Chapter 13. H1 -Galerkin Methods for the Laplace and Heat Equations
  19. References.
  20. Subject Index