Analysis of the Performance of Mixed Finite Element Methods.

Abstract : The investigator was able to prove an optimal error estimate for approximating functions in sobolev spaces using a space of pieceurse polynomial functions (based on the p-version of the finite element method). Optimal approximation results were also obtained for the h-p version of the finite element method using quasiuniform meshes. Papers accepted for publication during this period of effort included such titles as The optimal convergence rate of the p-version of the finite element methods, Some optimal approximation results with applications to the h-p-, and h-p versions of the finite element method, and The h-p version of the finite element method with quasi-uniform meshes. Keywords: Stability; Polynomials; Lagrange multipliers; Laplace equations.