HIGH ORDER DISCONTINUOUS GALERKIN METHODS FOR 1D PARABOLIC EQUATIONS

摘要

Development of accurate and efficient numerical methods is an important task for many research areas. This work presents the numerical study of the Discontinuous Galerkin Finite Element (DG) methods in space and various ODE solvers in time applied to 1D parabolic equation. In particular, we study the numerical convergence and computational efficiency of the Backward Euler (BE) in time and high order DG in space methods vs. the numerical convergence and the computational efficiency of the DG in time and space methods.