The Direct Discontinuous Galerkin (DDG) Methods for Diffusion Problems

摘要: A new discontinuous Galerkin finite element method for solving diffusion problems is introduced. Unlike the traditional local method, scheme called direct (DDG) based on weak formulation solutions of parabolic equations in each computational cell and lets cells communicate via numerical flux $\widehat{u_x}$ only. We propose a general formula solution derivative, which consistent conservative; we then introduce concept admissibility to identify class fluxes so that nonlinear stability both one-dimensional (1D) multidimensional are ensured. Furthermore, when applying DDG with admissible 1D linear case, $k$th order accuracy an energy norm proven using degree polynomials. The has advantage easier implementation efficient computation solution. series examples presented demonstrate high method. In particular, study performance different fluxes.