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Mixed finite element method for a second order Dirichlet boundary control problem

Published: 01 April 2023 Publication History

Abstract

The main aim of this article is to analyze mixed finite element method for the second order Dirichlet boundary control problem. We develop both a priori and a posteriori error analysis using the energy space based approach. We obtain optimal order a priori error estimates in the energy norm and L 2-norm with the help of auxiliary problems. The reliability and the efficiency of proposed a posteriori error estimator is discussed using the Helmholtz decomposition. Numerical experiments are presented to confirm the theoretical findings.

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Published In

cover image Computers & Mathematics with Applications
Computers & Mathematics with Applications  Volume 135, Issue C
Apr 2023
207 pages

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Pergamon Press, Inc.

United States

Publication History

Published: 01 April 2023

Author Tags

  1. Mixed finite element method
  2. A priori error estimates
  3. A posteriori error estimates
  4. Optimal control
  5. Dirichlet boundary control
  6. Raviart-Thomas element

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