A C⁰ Interior Penalty Method for the von Kármán Equations

In this dissertation we develop a C⁰ interior penalty method for the von Kármán equations for nonlinear elastic plates. We begin with a brief survey on frequently used finite element methods for the von Kármán equations. After addressing some topics from functional analysis in the preliminaries, we present existence, uniqueness and regularity results for the solutions of the von Kármán equations in Chapter 3. In the next chapter we review the C⁰ interior penalty method for the biharmonic problem. Motivated by these results, we propose a C⁰ interior penalty method for the linearized von Kármán equations in Chapter 5 and show the well-posedness and stability of this method. We then introduce the new C⁰ interior penalty method for von Kármán equations, and establish the corresponding a priori error estimate by a fixed point argument. Numerical examples are presented that confirm the theoretical results.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2011

Author dc:creator

• Reiser, Armin Karl

• nonconforming finite element methods
• interior penalty methods
• nonlinear elastic plates
• von Karman equations

Statement dc:rights

• withheld
• Secure the entire work for patent and/or proprietary purposes for a period of one year. Student has submitted appropriate documentation which states: During this period the copyright owner also agrees not to exercise her/his ownership rights, including public use in works, without prior authorization from LSU. At the end of the one year period, either we or LSU may request an automatic extension for one additional year. At the end of the one year secure period (or its extension, if such is requested), the work will be released for access worldwide.

Identifier

etd-11042011-125339
https://repository.lsu.edu/gradschool_dissertations/615

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-1614