ROBUST A POSTERIORI ERROR ESTIMATOR FOR LOWEST-ORDER FINITE ELEMENT METHODS OF INTERFACE PROBLEMS

다국어 초록 (Multilingual Abstract)

In this paper we analyze an a posteriori error estimator based on flux recovery for lowest-order finite element discretizations of elliptic interface problems. The flux recovery considered here is based on averaging the discrete normal fluxes and/or tangential derivatives at midpoints of edges with weight factors adapted to discontinuous coefficients. It is shown that the error estimator based on this flux recovery is equivalent to the error estimator of Bernardi and Verfürth based on the standard edge residuals uniformly with respect to jumps of the coefficient between subdomains. Moreover, as a byproduct, we obtain slightly modified weight factors in the edge residual estimator which are expected to produce more accurate results.

목차 (Table of Contents)

• ABSTRACT
• 1. INTRODUCTION
• 2. NOTATION AND FINITE ELEMENT METHODS
• 3. EDGE RESIDUAL ERROR ESTIMATORS
• 4. RECOVERY-BASED ERROR ESTIMATOR
• 5. NUMERICAL RESULTS
• REFERENCES