hphp-Adaptive least squares spectral element method for hyperbolic partial differential equations

This paper describes a hp  -adaptive spectral element formulation which is used to discretize the weak formulation obtained by minimizing the residuals in the L2L2-norm. The least-squares error indicator will be briefly discussed. Refinement of the numerical approximation is based on an estimate of the regularity of the underlying exact solution; if the underlying exact solution is sufficiently smooth polynomial enrichment is employed, in areas with limited regularity hh-refinement is used. For this purpose the Sobolev regularity is estimated. Functionally and geometrically non-conforming neighbouring elements are patched together using so-called mortar elements. Results of this approach are compared to uniform h- and p-refinement for a linear advection equation.