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

by L. Demkowicz and K. Gerdes and Ch. Schwab and A. Bajer and T. Walsh

(Report number 1997-17)

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

@Techreport{DGSBW97_222,
  author = {L. Demkowicz and K. Gerdes and Ch. Schwab and A. Bajer and T. Walsh},
  title = {HP90: A general and flexible Fortran 90 $hp$-FE code},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1997-17},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1997/1997-17.pdf },
  year = {1997}
}

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