Numerical Approximation of Partial Differential Equations book cover

Numerical Approximation of Partial Differential Equations

This selection of papers is concerned with problems arising in the numerical solution of differential equations, with an emphasis on partial differential equations. There is a balance between theoretical studies of approximation processes, the analysis of specific numerical techniques and the discussion of their application to concrete problems relevant to engineering and science. Special consideration has been given to innovative numerical techniques and to the treatment of three-dimensional and singular problems. These topics are discussed in several of the invited papers.The contributed papers are divided into five parts: techniques of approximation theory which are basic to the numerical treatment of differential equations; numerical techniques based on discrete processes; innovative methods based on polynomial and rational approximation; variational inequalities, conformal transformation and asymptotic techniques; and applications of differential equations to problems in science and engineering.

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Published: February 1987

Imprint: North-holland

ISBN: 978-0-444-70140-4

Contents

  • Invited Papers: Recent Progress in the Two-Dimensional Approximation of Three Dimensional Plate Models in Nonlinear Elasticity (P.G. Ciarlet). Formulation of Alternating-Direction Iterative Methods for Mixed Methods in Three Space (J. Douglas, Jr., R. Durán, P. Pietra). Iterative Methods for Singular Systems (I. Marek). On Different Numerical Methods to Solve Singular Boundary Problems (F. Michavila). Some Numerical Techniques for the Solution of Problems Related to Semiconductor Devices (J.J.H. Miller). Recent Progress in the Numerical Treatment of Singular Problems for Partial Differential Equations with Techniques Based on the Tau Method (E.L. Ortiz). Present State and New Trends in Parallel Computation (R. Portaencasa, C. Vega). Finite Element Methods for Treating Problems Involving Singularities, with Applications to Linear Elastic Fracture (J.R. Whiteman). Finite Element Solution of the Fundamental Equations of Semiconductor Devices (M. Zlámal). Plus 28 contributed papers.

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