EXtended hybridizable discontinuous Galerkin for incompressible flow problems with unfitted meshes and interfaces

Abstract

SummaryThe eXtended hybridizable discontinuous Galerkin (X‐HDG) method is developed for the solution of Stokes problems with void or material interfaces. X‐HDG is a novel method that combines the hybridizable discontinuous Galerkin (HDG) method with an eXtended finite element strategy, resulting in a high‐order, unfitted, superconvergent method, with an explicit definition of the interface geometry by means of a level‐set function. For elements not cut by the interface, the standard HDG formulation is applied, whereas a modified weak form for the local problem is proposed for cut elements. Heaviside enrichment is considered on cut faces and in cut elements in the case of bimaterial problems. Two‐dimensional numerical examples demonstrate that the applicability, accuracy, and superconvergence properties of HDG are inherited in X‐HDG, with the freedom of computational meshes that do not fit the interfaces