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Objectives

The goals of this thesis are:

To show how polymorphic elements can be built and interfaced to enhance efficiency of the unstructured spectral element method (USEME).
To demonstrate how Object-Oriented Programming can be used with minimal overhead to provide a flexible toolkit for the polymorphic USEME.
To provide theoretical and numerical evidence that USEME retains good approximation properties even when very distorted meshes are used.
To implement a semi-implicit Galerkin USEME scheme for the equations of incompressible Navier-Stokes and magnetohydrodynamics (MHD) in the computer code .
To investigate the effectiveness of USEME applied to moving domain problems using the ALE formulation.
To implement a fully explicit discontinuous Galerkin method (DGM) USEME scheme for the equations of compressible Navier-Stokes and magnetohydrodynamics in the computer code .
To demonstrate accuracy for the above methods.

T. Warburton
10/24/1998