A posteriori error estimates for H¹-Galerkin mixed finite-element method for parabolic problems

Abstract

The purpose of this article is to derive a posteriori error estimates for the H ¹-Galerkin mixed finite element method for parabolic problems. We study both semidiscrete and fully discrete a posteriori error analyses using standard energy argument. A fully discrete a posteriori error analysis based on the backward Euler method is analysed and upper bounds for the errors are derived. The estimators yield upper bounds for the errors which are global in space and time. Our analysis is based on residual approach and the estimators are free from edge residuals.

Keywords:

• parabolic problems
• H ¹-Galerkin mixed finite-element method
• semidiscrete
• fully discrete
• a posteriori error estimates

AMS Subject Classifications:

• 65M60
• 65M15
• 65M12

Acknowledgements

The authors thank the referee for his valuable comments and suggestions that improved this article.