Flux recovery scheme for elliptic interface problems

Abstract

This paper introduces a flux recovery algorithm that ensures the continuity of the flux at the interface and improves its accuracy. At each subdomain created by an interface, the gradient is recovered using the polynomial preserving recovery method and a weight is given to each subdomain based on these recovered gradients. Then from these recovered gradients and subdomain weights, we form what we call a corrected recovered gradient that is exploited to construct the recovered flux at the interface. An error estimator that is based on the recovered flux is formulated for an adaptive refinement scheme that improves the accuracy of the flux near the interface. We present the numerical results of applying the proposed scheme to some two-dimensional experiments with different types of interfaces.

Keywords

• Flux recovery
• Elliptic interface problems
• Corrected recovered gradient
• Adaptive finite element