Recovery-Based Error Estimator for Interface Problems: Conforming Linear Elements

Authors:
Zhiqiang Cai;Shun Zhang
Affiliations:
zcai@math.purdue.edu and zhang@math.purdue.edu;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2009

Citing 0
Cited 6

Guaranteed and Fully Robust a posteriori Error Estimates for Conforming Discretizations of Diffusion Problems with Discontinuous Coefficients

Journal of Scientific Computing
Recovery-Based Error Estimators for Interface Problems: Mixed and Nonconforming Finite Elements

SIAM Journal on Numerical Analysis
Flux Recovery and A Posteriori Error Estimators: Conforming Elements for Scalar Elliptic Equations

SIAM Journal on Numerical Analysis
Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations

SIAM Journal on Numerical Analysis
Robust Equilibrated Residual Error Estimator for Diffusion Problems: Conforming Elements

SIAM Journal on Numerical Analysis
Multiphysics simulations: Challenges and opportunities

International Journal of High Performance Computing Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper studies a new recovery-based a posteriori error estimator for the conforming linear finite element approximation to elliptic interface problems. Instead of recovering the gradient in the continuous finite element space, the flux is recovered through a weighted $L^2$ projection onto $H(\mathrm{div})$ conforming finite element spaces. The resulting error estimator is analyzed by establishing the reliability and efficiency bounds and is supported by numerical results. This paper also proposes an adaptive finite element method based on either the recovery-based estimators or the edge estimator through local mesh refinement and establishes its convergence. In particular, it is shown that the reliability and efficiency constants as well as the convergence rate of the adaptive method are independent of the size of jumps.