Location
DC 1304
Candidate
Joaquín Valenzuela | Applied Mathematics, University of Waterloo
Title
Towards an a-priori analysis for hybridizable discontinuous Galerkin methods on anisotropic meshes
Abstract
The finite element method has been used for many decades in the solution of partial differential equations (PDE). The mesh of the domain is an important aspect of the finite element method and plays a large role in the accuracy of the finite element solution. One big assumption on the family of meshes used for the analysis is the fact that the aspect ratio of each element is bounded, i.e., that the mesh is isotropic. However, isotropic meshes are often unsuitable for singularly perturbed problems. For such problems the solution may change very rapidly, and more and finer elements are needed in areas of large gradients to obtain a good quality solution under this paradigm. The computationally efficient way to address this problem is by using anisotropic meshes, which are colloquially known to have "stretched" elements. In this work we present some recent literature results on anisotropic interpolation error estimates, initial results for the a-priori analysis of a hybridizable discontinuous Galerkin (HDG) method for the advection-diffusion equation in three dimensions, and some initial results regarding a discrete functional analysis on discontinuous Galerkin (DG) spaces on anisotropic meshes.