Report 1997-17

HP90: A general and flexible Fortran 90 $hp$-FE code

L. Demkowicz, K. Gerdes, C. Schwab, A. Bajer and T. Walsh

Abstract: A general 2D-$hp$-adaptive Finite Element (FE) implementation inFortran 90 is described. The implementation is based on an abstractdata structure, which allows to incorporate the full $hp$-adaptivityof triangular and quadrilateral finite elements.The $h$-refinement strategies are based on $h2$-refinement ofquadrilaterals and $h4$-refinement of triangles. For $p$-refinementwe allow the approximation order to vary within any element. The meshrefinement algorithms are restricted to 1-irregular meshes. Anisotropicand geometric refinement of quadrilateral meshes is made possible by additionally allowing double constrained nodes in rectangles.The capabilities of this $hp$-adaptive FE package are demonstratedon various test problems.

Keywords: $hp$ finite element method, spectral element method, constrained approximation, anisotropic mesh refinement

Paper: Available as PDF (1 MB) or as hardcopy to order reports@sam.math.ethz.ch.

Publishing information: Computing and Visualization in Science 1 (1998), pp. 145-163