High Order Discontinuous Cut Finite Element Methods for Linear Hyperbolic Conservation Laws with an Interface

Abstract We develop a family of cut finite element methods different orders based on the discontinuous Galerkin framework, for hyperbolic conservation laws with stationary interfaces in both one and two space dimensions, moving dimension. Interface conditions are imposed weakly so that stability ensured. A CutFEM elements is developed coupled to standard explicit time stepping schemes linear advection problems acoustic wave problem interfaces. In case interfaces, we propose space-time problems. show proposed conservative energy stable. For interface an priori error estimate proven. Numerical computations dimensions support analysis, addition demonstrate have expected accuracy.