Multi-Grid Continuation and Spurious Solutions for Nonlinear Boundary Value Problems.

Abstract

Recently the author together with R. Bank has developed, implemented and successfully applied a continuation technique for the numerical solution of parameter-dependent nonlinear elliptic boundary value problems. The method was integrated into an existing multi-grid package based on an adaptive finite element discretization. This document present the continuation method and proves an important theoretical result for the corrector iteration. For the Bratu problem - delta u = lambda e sub u on the square with homogeneous Dirichlet conditions it is shown how spurious solutions may be encountered while computing relevant solutions, how the program handles those and how it allows to detect them.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1986
Accession Number
ADA173081

Entities

People

  • Hans D. Mittelmann

Organizations

  • University of Arizona

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Boundary Value Problems
  • Classification
  • Differential Equations
  • Equations
  • Formulas (Mathematics)
  • Hilbert Space
  • Integral Equations
  • Iterations
  • Mathematics
  • Polynomials
  • Riccati Equation
  • Security
  • Simulations
  • Universities
  • Variational Principles

Fields of Study

  • Mathematics

Readers

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