Approximation and Numerical Analysis of Nonlinear Equations of Evolution.

Abstract

Important results were obtained in four areas: (1) Existence theorems, approximation theorems, a priori error estimates, numerical schemes, and finally computer codes were developed for the analysis of one-and two-dimensional, one- and two-phase Stefan problems characterized by variational inequalities; (2) Existence theorems, uniqueness theorems, theorems on the stability and asymptotic stability of solutions, and regularity of solutions were developed for a large class of nonlinear, convective diffusion problems characterized by pseudo-monotone operators; (3) A priori error estimates for Galerkin and Faedo-Galerkin approximations (defined, in general, by finite element methods) were established for nonlinear convection diffusion problems involving general pseudomonotone operators; and (4) Existence theorems were obtained for a large class of nonlinear, degenerate evolution equations with solutions involving free boundaries. Applications to porous media and two-phase Stephan problems were completed. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 31, 1980
Accession Number
ADA082452

Entities

People

  • J. T. Oden

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Banach Space
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Differential Equations
  • Engineering
  • Equations
  • Finite Element Analysis
  • Heat Energy
  • Mathematical Analysis
  • Numerical Analysis
  • Phase Transformations
  • Scientists
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra