Third Order Maximum-principle-satisfying Direct Discontinuous Galerkin Methods for Time Dependent Convection Diffusion Equations on Unstructured Triangular Meshes

Download or read book Third Order Maximum-principle-satisfying Direct Discontinuous Galerkin Methods for Time Dependent Convection Diffusion Equations on Unstructured Triangular Meshes written by and published by . This book was released on 2015 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8], [9], [19] and [21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair ([beta]0, [beta]1) in the numerical flux formula, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. As a result, a sequence of numerical examples are carried out to demonstrate the accuracy and capability of the maximum-principle-satisfying limiter.