Parallel h-p Spectral Element Method for Elliptic Problems on Polygonal Domains

Spectral element methods (SEM) exhibit exponential convergence only when the solution of the problem is sufficiently regular. However, the solution develops a singularity when the boundary of the domain is non-smooth. The accuracy of the SEM is then deteriorated and they offer no advantage over low order methods. Such problems frequently occur in many important physical applications, for example in structural mechanics. A new h-p spectral element method is presented which resolves this form of singularity and gives asymptotically faster results than conventional methods, while retaining the same order of convergence. Moreover, the computational algorithm is devised to harness the potential of widely available parallel computers.