Title
Resolvent Estimates and Discrete Maximal Parabolic Regularity for Galerkin Finite Element Methods
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.
Recommended Citation
Allaire, Kyle, "Resolvent Estimates and Discrete Maximal Parabolic Regularity for Galerkin Finite Element Methods" (2020). Doctoral Dissertations. 2584.
https://digitalcommons.lib.uconn.edu/dissertations/2584