SUPG space-time scheme on anisotropic meshes for general parabolic equations

In this paper, a stabilized space-time finite element scheme on anisotropic quadrilateral meshes for general linear parabolic problems is considered. The scheme is devised on the basis of a unified space-time variational formulation, and uses continuous piece-wise polynomial spaces. The stabilization is achieved by incorporating Streamline-Upwind Petrov–Galerkin (SUPG) techniques. Defining appropriately the stability coefficients, we initially show anisotropic interpolation estimates and then a priori error estimates by following a classical finite element methodology. A series of numerical examples illustrates the theoretical findings.