Toward a universal adaptive finite element strategy part 3. design of meshes

Abstract In this third paper in our series, the issue of designing h-p meshes which are optimal in some sense is addressed. Criteria for h-p meshes are derived which are based on the idea of minimizing the estimated error over a mesh with a fixed number of degrees-of-freedom. An optimization algorithm is developed based on these criteria and is applied to several model one-dimensional and two-dimensional elliptic boundary-value problems. Numerical results indicate that the approach can lead to exponential rates-of-convergence.