Abstract

Higher order finite elements present certain challenges for multilevel methods. Such matrices have more nonzero elements and special block structure. In the case of $h-p$ adaptive methods, the block structure is more complicated. In this work we present a simple two level solver for such systems, that exploits these special properties. The convergence rate is (empirically) multigrid-like, at least up to piecewise polynomials of degree nine. Numerical illustrations demonstrate its robustness on a wide variety of problems, including convection-diffusion and Helmholtz equations.