A Posteriori Error Estimates of Finite Element Solutions of Parametrized Nonlinear Equations

Abstract

Nonlinear differential equations with parameters are called parametrized nonlinear equations. This paper studies a posteriori error estimates of finite element solutions of second order parametrized strongly nonlinear equations in divergence form on one-dimensional bounded intervals. In the previous paper by the authors, the finite element solutions are defined, and several a priori estimates are proved on regular branches and on branches around turning points. Using obtained a priori error estimates, we obtain several practical a posteriori error estimates which are asymptotically exact. Some numerical examples are given.... Parametrized nonlinear equations, Fredholm operators, Regular branches, Turning points, Finite element solutions, A priori and a posteriori error estimates.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1992
Accession Number
ADA260014

Entities

People

  • Ivo Babuška
  • Takuya Tsuchiya

Organizations

  • University of Maryland

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  • Banach Space
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  • Mathematics

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  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
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