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We present a study of the application of dual-weighted residual (DWR) error estimation in the context of stabilized mixed finite element discretizations for a certain Poisson problem. The study specifically investigates the enforcement of a Dirichlet condition on a closed, smooth curve within a two-dimensional domain. The main focus lies in the derivation of a practical error representation for stabilized Galerkin methods. The paper covers the mixed finite element method, its stabilization, and the a posteriori error estimator. In addition, the paper includes numerical results that demonstrate the effectiveness of the stabilization technique and the efficiency of the adaptive method.

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Goal-Oriented Error Estimates for Adaptive Mixed Finite Element Methods

  • 会议论文

  • 发表日期：

    2025年

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  • Lothar Banz,
  • Andreas Rademacher,
  • Dominika Thiede

摘要

We present a study of the application of dual-weighted residual (DWR) error estimation in the context of stabilized mixed finite element discretizations for a certain Poisson problem. The study specifically investigates the enforcement of a Dirichlet condition on a closed, smooth curve within a two-dimensional domain. The main focus lies in the derivation of a practical error representation for stabilized Galerkin methods. The paper covers the mixed finite element method, its stabilization, and the a posteriori error estimator. In addition, the paper includes numerical results that demonstrate the effectiveness of the stabilization technique and the efficiency of the adaptive method.