Space-Time Petrov-Discontinuous Galerkin Finite Element Method for Solving Linear Convection-Diffusion Problems

Abstract

Abstract The paper presents the theory of the space-time Petrov-discontinuous Galerkin finite element (PDGFE) method for the discretization of the nonstationary linear convection-diffusion problems. The PDGFE method is modified for the discontinuous Galerkin finite element (DGFE) method in the case of the symmetric interior penalty Galerkin (SIPG) scheme. PDGFE method is applied separately in space using different space gride on different time levels. We prove the properties of the bilinear form aPD, m (u, ν) (V − elliptic and continuity) stability and prove the approximate solution converges with the error of order o (h 2 + τ 3). A numerical experiment is carried out to confirm the theoretical conclusions.