Numerical Methods for Partial Differential Equations : Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin-Madison, October 23-25, 1978

Numerical Methods for Partial Differential Equations is a collection of papers dealing with techniques and practical solutions to problems concerning continuum mechanics, fluid dynamics, and plasma physics. One paper discusses the important considerations that lead to an efficient nonlinear dynamic finite element analysis using improved analysis techniques. Another paper describes the results obtained from fully discrete methods of higher order in time (order 3 and 4) for second order parabolic initial boundary value problems in which the equations have time dependent (or nonlinear) coefficients. Another paper reviews concepts of ellipticity of finite-difference approximations to general elliptic partial differential systems, with examples utilizing Cauchy-Riemann equations or Navier-Stokes equations. One paper describes fluid-dynamic computing using basic equations, boundary conditions, time dependent gas dynamics, shock waves, stream-function-vorticity methods, and an example on the formation of a spherical vortex. Another paper evaluates a specific problem arising in the study of the equilibrium of plasma confined in a machine of the Tokomak type. The collection is suitable for mathematicians, physicists, and investigators in the field of continuum mechanics, fluid dynamics, plasma physics. Content: Academic Press Rapid Manuscript Reproduction, Page ii Front Matter, Page iii Copyright, Page iv CONTRIBUTORS, Page vii PREFACE, Page ix, Seymour V. Parter Finite Element Formulation, Modeling, and Solution of Nonlinear Dynamic Problems, Pages 1-40, Klaus-Jürgen Bathe Discrete Methods for Parabolic Equations with Time-Dependent Coefficients, Pages 41-52, James H. Bramble Multigrid Solutions to Elliptic Flow Problems, Pages 53-147, Achi Brandt, Nathan Dinar Computational Fluid Dynamics, Pages 149-175, C.K. Chu The Numerical Solution of a Degenerate Variational Inequality, Pages 177-191, Colin W. Cryer Simplified Solution Algorithms for Fluid Flow Problems, Pages 193-211, C.W. Hirt Numerical Methods for Hyperbolic Partial Differential Equations, Pages 213-254, H.-O. Kreiss Constructing Stable Difference Methods for Hyperbolic Equations, Pages 255-271, Joseph Oliger Spectral Methods for Problems in Complex Geometrics, Pages 273-305, Steven A. Orszag Numerical Problems in Plasma Physics, Pages 307-327, R. Temam INDEX, Pages 329-332 Conducted By The Mathematics Research Center, The University Of Wisconsin--madison, October 23-25, 1978 ; Edited By Seymour V. Parter. Includes Bibliographies And Index.