Doctor of Philosophy (PhD)
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.
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Reiser, Armin Karl, "A C0 Interior Penalty Method for the von Kármán Equations" (2011). LSU Doctoral Dissertations. 615.
Brenner, Susanne C.