Third order Maximum-Principle-Satisfying Direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangle mesh

摘要

We develop 3rd order maximum-principle-satisfying direct discontinuousGalerkin methods [8, 9, 19, 21] for convection diffusion equations onunstructured triangular mesh. We carefully calculate the normal derivativenumerical flux across element edges and prove that, with proper choice ofparameter pair $(\beta_0,\beta_1)$ in the numerical flux, the quadraticpolynomial solution satisfies strict maximum principle. The polynomial solutionis bounded within the given range and third order accuracy is maintained. Thereis no geometric restriction on the meshes and obtuse triangles are allowed inthe partition. A sequence of numerical examples are carried out to demonstratethe accuracy and capability of the maximum-principle-satisfying limiter.