Location
MC 6460
Candidate
Joaquin Valenzuela Diaz | Applied Mathematics, University of Waterloo
Title
A hybridizable discontinuous Galerkin method for the advection-diffusion problem in the advection-dominated limit on three dimensional 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 the study of a hybridizable discontinuous Galerkin (HDG) scheme for the solution of the advection-diffusion system using anisotropic meshes on a three dimensional domain.