Triangular Spectral Element Methods for Geophysical Fluid Dynamics Applications

This work discusses spectral element methods in R 2 on triangular subdomains for application to problems in geophysical fluid dynamics. Methods using triangles as their subdomains are of interest because it is easier to break irregularly shaped domains into triangles than the more commonly used rectangular subdomains. Dubiner has derived a basis which is optimal for many engineering applications where diffusion plays an important role. His `modified' basis gives sparse matrices for both the weight matrix and the Laplacian operator, making it ideal for semi-implicit schemes which treat diffusion implicitly and advection explicitly. Large scale geophysical fluid dynamic simulations have different requirements than for engineering applications; methods optimal for one class of problems are not necessarily optimal for the other. This work uses a different basis set, an `interior-orthogonal' basis, which retains the most important properties of his `modified' basis, but gives a weight mat..