An eXtended HDG method for Darcy-Stokes-Brinkman interface problems

TL;DR

This paper introduces an extended hybridizable discontinuous Galerkin method for efficiently solving Darcy-Stokes-Brinkman interface problems in multiple dimensions, with proven accuracy and robustness.

Contribution

It develops an interface-unfitted X-HDG method with optimal error estimates for Darcy-Stokes-Brinkman problems, enhancing computational flexibility and accuracy.

Findings

Optimal error estimates are established for the proposed scheme.

Numerical experiments confirm the theoretical accuracy and robustness.

The method effectively handles interface problems in 2D and 3D.

Abstract

This paper proposes an interface/boundary-unfitted eXtended hybridizable discontinuous Galerkin (X-HDG) method for Darcy-Stokes-Brinkman interface problems in two and three dimensions. The method uses piecewise linear polynomials for the velocity approximation and piecewise constants for both the velocity gradient and pressure approximations in the interior of elements inside the subdomains separated by the interface, uses piecewise constants for the numerical traces of velocity on the inter-element boundaries inside the subdomains, and uses piecewise constants or linear polynomials for the numerical traces of velocity on the interface. Optimal error estimates are derived for the interface-unfitted X-HDG scheme. Numerical experiments are provided to verify the theoretical results and the robustness of the proposed method.