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Complementary error bounds for elliptic systems and applications

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
219
Issue
13
Identifiers
DOI: 10.1016/j.amc.2011.05.108
Keywords
  • A Posteriori Error Estimates
  • Guaranteed Error Bounds
  • Complementarity
  • Dual Finite Element Methods
  • Elliptic Systems
  • Elasticity
  • Diffusion–Convection–Reaction Problems
Disciplines
  • Chemistry

Abstract

Abstract This contribution derives guaranteed upper bounds of the energy norm of the approximation error for linear elliptic partial differential systems. We generalize the complementarity error estimates known for scalar elliptic problems to general diffusion–convection–reaction linear elliptic systems. For systems we prove analogous properties of these error bounds as for the scalar case. A brief description how the presented general theory applies to linear elasticity is included as well as an application to chemical systems with reactions of at most first order. Numerical experiments showing the sharpness of the obtained upper bounds and their behavior in the adaptive procedure are presented, too.

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