Mortar-based entropy-stable discontinuous Galerkin methods on non-conforming quadrilateral and hexahedral meshes

Abstract

High-order entropy-stable discontinuous Galerkin (DG) methods for nonlinear conservation laws reproduce a discrete entropy inequality by combining entropy conservative finite volume fluxes with summation-by-parts (SBP) discretization matrices. In the DG context, on tensor product (quadrilateral and hexahedral) elements, SBP matrices are typically constructed by collocating at Lobatto quadrature points. Recent work has extended the construction of entropy-stable DG schemesto collocation at more accurate Gauss quadrature points [1].

Energy stable and accurate coupling of finite element methods and finite difference methods

“…A simplest example of this idea is shown in Example C.1. The authors found that the technique sketched here is related to the mortar method, see [14,3], the mortar method in SBP context [6,11].…”

“…The boundary condition (4) imposes nonlinear stability to (1) since bounded energy is followed. Indeed, inserting (4) into (6) with zero boundary data…”

Energy stable and accurate coupling of finite element methods and finite difference methods

“…A simplest example of this idea is shown in Example A.1. The authors found that the technique sketched here is related to the mortar method, see [12,3], the mortar method in SBP context [6,10]. Example A.1.…”

“…It becomes apparent that the boundary condition (4) imposes nonlinear stability to (1) since bounded energy is followed. Indeed, inserting (4) into (6) with zero boundary data ≡ 0 gives…”