First Advisor

Jeffrey Ovall

Term of Graduation

Fall 2020

Date of Publication

11-18-2020

Document Type

Dissertation

Degree Name

Doctor of Philosophy (Ph.D.) in Mathematical Sciences

Department

Mathematics and Statistics

Language

English

Subjects

Maxwell equations, Discretization (Mathematics), Finite element method

DOI

10.15760/etd.7471

Physical Description

1 online resource (vii, 111 pages)

Abstract

The aim of our work is to construct provably efficient and reliable error estimates of discretization error for Nédélec (edge) element discretizations of Maxwell's equations on tetrahedral meshes. Our general approach for estimating the discretization error is to compute an approximate error function by solving an associated problem in an auxiliary space that is chosen so that:

-Efficiency and reliability results for the computed error estimates can be established under reasonable and verifiable assumptions.

-The linear system used to compute the approximate error function has condition number bounded independently of the discretization parameter.

In many applications, it is some functional of the solution that is primarily of interest. In such cases, it makes sense to estimate and control discretization error with respect to this functional, rather than with respect to a global norm. We will also develop auxiliary subspace techniques for this kind of goal-oriented error estimation.

Rights

©2020 Ahmed El sakori

In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).

Persistent Identifier

https://archives.pdx.edu/ds/psu/34447

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