First Advisor

Jay Gopalakrishnan

Date of Publication

Spring 5-10-2016

Document Type

Dissertation

Degree Name

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

Department

Mathematics and Statistics

Language

English

Subjects

Galerkin methods, Numerical analysis

DOI

10.15760/etd.2912

Physical Description

1 online resource (vii, 103 pages)

Abstract

This dissertation presents a duality theorem of the Aubin-Nitsche type for discontinuous Petrov Galerkin (DPG) methods. This explains the numerically observed higher convergence rates in weaker norms. Considering the specific example of the mild-weak (or primal) DPG method for the Laplace equation, two further results are obtained. First, for triangular meshes, the DPG method continues to be solvable even when the test space degree is reduced, provided it is odd. Second, a non-conforming method of analysis is developed to explain the numerically observed convergence rates for a test space of reduced degree. Finally, for rectangular meshes, the test space is reduced, yet the convergence is recovered regardless of parity.

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Persistent Identifier

http://archives.pdx.edu/ds/psu/17472

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