Mathematical Aspects of Finite Elements in Partial Differential Equations - 1st Edition - ISBN: 9780122083501, 9781483268071

Mathematical Aspects of Finite Elements in Partial Differential Equations

1st Edition

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

Editors: Carl de Boor
eBook ISBN: 9781483268071
Imprint: Academic Press
Published Date: 1st January 1974
Page Count: 430
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Description

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.

Table of Contents


Preface

Higher Order Local Accuracy by Averaging in the Finite Element Method

Convergence of Nonconforming Methods

Some Convergence Results for Galerkin Methods for Parabolic Boundary Value Problems

On a Finite Element Method for Solving the Neutron Transport Equation

A Mixed Finite Element Method for the Biharmonic Equation

A Dissipative Galerkin Method for the Numerical Solution of First Order Hyperbolic Equations

C1 Continuity Via Constraints for 4th Order Problems

Finite Element and Finite Difference Methods for Hyperbolic Partial Differential Equations

Solution of Problems with Interfaces and Singularities

The Construction and Comparison of Finite Difference Analogs of Some Finite Element Schemes

L2 Error Estimates for Projection Methods for Parabolic Equations in Approximating Domains

An H-1-Galerkin Procedure for the Two-Point Boundary Value Problem

H1-Galerkin Methods for the Laplace and Heat Equations

Index

Details

No. of pages:
430
Language:
English
Copyright:
© Academic Press 1974
Published:
Imprint:
Academic Press
eBook ISBN:
9781483268071

About the Editor

Carl de Boor