Analysis of Adaptive Finite Element Methods

Abstract: This thesis is concerned with the analysis and design of adaptive finite element methods for a variety of differential equations in mechanics and physics, including linear and semilinear elliptic equations, eigenvalue problems, the stationary Navier-Stokes equations, and Hamiltonian systems. The analysis focuses on sharp a posteriori error estimates, sharp a priori error estimates, stability properties, and the design of adaptive algorithms. The performance of the adaptive methods is illustrated by numerical examples.