Andrei Maxim

Ph.D. in Mathematics (May 2007)

First Position

Assoc. derivatives analysis, Goldman Sachs, London

Dissertation

Aspects of the Finite Element Method for Elliptic Partial Differential Equations

Advisor

Lars B. Wahlbin

Research Area

Numerical solutions of partial differential equations

Abstract

Results in two different areas of the finite element method are proved.

First we study an a posteriori error estimator for second-order elliptic problems.  The estimator is based on the equilibrated residual method.  We prove that this estimator is asymptotically exact on O(h1+α) meshes.

Second, we study the approximation properties of the Morley element for the plate bending problem with clamped boundary conditions on a convex domain with smooth curved boundary.  Building on the work of Schatz, we establish localized pointwise error estimates for the second derivatives.  In the process, we also derive global and local error estimates in L2-based norms.