Gradient recovery for elliptic interface problem: I. body-fitted mesh

2016/07/20 by Hailong Guo, Xu Yang, Guo, Hailong +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1607.05898

openalex publication_date 2016/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose a novel gradient recovery method for elliptic interface problem using body-fitted mesh in two dimension. Due to the lack of regularity of solution at interface, standard gradient recovery methods fail to give superconvergent results, and thus will lead to overrefinement when served as a posteriori error estimator. This drawback is overcome by designing an immersed gradient recovery operator in our method. We prove the superconvergence of this method for both mildly unstructured mesh and adaptive mesh, and present several numerical examples to verify the superconvergence and its robustness as a posteriori error estimator.

Cited by

• Superconvergence analysis of partially penalized immersed finite element method

Related

• Elliptic interface problem approximated by CutFEM: I. Conservative flux recovery and numerical validation of adaptive mesh refinement
• Accurate gradient computations at interfaces using finite element methods
• An adaptive high-order unfitted finite element method for elliptic interface problems
• Recovery Techniques for Finite Element Methods
• An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation, Part II. Piecewise-smooth interfaces