Date of Award

Spring 1-1-2018

Document Type


Degree Name

Doctor of Philosophy (PhD)

First Advisor

John A. Evans

Second Advisor

Peter Hamlington

Third Advisor

Kenneth Jansen

Fourth Advisor

Daven Henze

Fifth Advisor

Franck Vernerey


This dissertation presents two novel contributions to the fields of isogeometric analysis and p-version finite elements. First, we present a framework for geometrically exact volumetric mesh generation. By leveraging ideas from both traditional mesh generation as well as isogeometric analysis, we develop a framework for volumetric mesh generation using rational Bernstein--Bézier discretizations. Within this framework, we provide a set of easily verifiable sufficient conditions for guaranteeing that a mesh will be geometrically exact. Second, we develop a complete theory of mesh quality for these rational Bernstein--Bézier elements. From this, we derive a set of easily computable mesh quality metrics for verifying that a rational Bernstein--Bézier discretization will be analysis suitable.