Date of Completion

8-8-2020

Embargo Period

8-8-2020

Keywords

Numerical Analysis, Finite Element Methods

Major Advisor

Dmitriy Leykekhman

Associate Advisor

Jeffrey Connors

Associate Advisor

Vasileios Chousionis

Field of Study

Mathematics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

We study space-time fully discrete maximal parabolic regularity for second order advection-diffusion operators. These estimates have many applications, including in the establishment of optimal a priori estimates in non Hilbert space norms. For time discretization, we use discontinuous Galerkin finite element methods that, in the simplest case of piecewise constant approximating functions, are equivalent to a modified backwards Euler time-stepping scheme. For discretization of the spatial variable, we analyze both continuous Galerkin (cG) and discontinuous Galerkin finite element methods (dG). Discontinuous Galerkin methods in space are analyzed because of our particular interest in the case where advection dominates diffusion, where stablized methods are needed.

Share

COinS