The Elastoplast Discontinuous Galerkin (EDG) method for the Navier–Stokes equations

A robust and adaptive recovery‐based discontinuous Galerkin method for the numerical solution of convection–diffusion equations

“…The strong approach consists in forcing the solution reconstruction to exactly satisfy a prescribed condition on the boundary. For example, Borrel and Ryan use this approach in their paper [17] on the elastoplast method. In this way, there is an error between the prescribed value and the solution reconstructed on the boundary, but this error vanishes in the limit of an infinite mesh refinement, with the same rate of the error in the interior of the domain.. From a practical point of view, it can be shown that the use of strong Dirichlet BC's can introduce stability limitations and spurious oscillations in the numerical solution (see, e.g.…”

“…The definition of the proper values in the ghost element can be carried out through symmetry 73 considerations between the boundary element and the ghost element. For example, Borrel and Ryan use this approach in their paper [17] on the elastoplast method. The problem is that this procedure could become ambiguous in the presence of curvilinear elements because in this case the boundary curve is not a symmetry axis between the boundary element and the ghost element.…”

“…He also proposed a 1D method, which can be extended to 2D on quadrilateral meshes via tensor products. Borrel and Ryan [17] proposed the elastoplast method in which the recovery idea is applied to a small rectangle overlapping the interface between two elements. French et al [18] introduced a modified recovery scheme that makes use of a penalty term.…”

“…The implementation is simplified with respect to the original recovery scheme (RDG1x). Borrel and Ryan [17] proposed the elastoplast method in which the recovery idea is applied to a small rectangle overlapping the interface between two elements. Numerical tests on unstructured grids show a convergence rate equal to p C 1, where p is the reconstruction order.…”

“…the work of Babuska and Zlamal [6]) and were used to compute the diffusive fluxes exchanged between adjacent elements. Borrel and Ryan [17] proposed the elastoplast method in which the recovery idea is applied to a small rectangle overlapping the interface between two elements. Bassi et al [2] proposed also a second version of their scheme (BR2) in which a compact stencil is obtained thanks to the use of lifting operators.…”