A DGFEM for Uniformly Elliptic Two Dimensional Oblique Boundary Value Problems

Abstract

In this paper we present and analyse a discontinuous Galerkin finite element method (DGFEM) for the approximation of solutions to elliptic partial differential equations in nondivergence form, with oblique boundary conditions, on curved domains. In "E. Kawecki, \emph{A DGFEM for Nondivergence Form Elliptic Equations with Cordes Coefficients on Curved Domains}", the author introduced a DGFEM for the approximation of solutions to elliptic partial differential equations in nondivergence form, with Dirichlet boundary conditions. In this paper, we extend the framework further, allowing for the oblique boundary condition. The method also provides an approximation for the constant occurring in the compatibility condition for the elliptic problems that we consider.