A general $\text{2D-} hp\text{-adaptive}$ Finite Element (FE) implementation in Fortran 90 is described. The implementation is based on an abstract data structure, which allows to incorporate the full $hp$-adaptivity of triangular and quadrilateral finite elements. The $h$-refinement strategies are based on $h2$-refinement of quadrilaterals and $h4$-refinement of triangles. For $p$-refinement we allow the approximation order to vary within any element. The mesh refinement algorithms are restricted to 1-irregular meshes. Anisotropic and 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 demonstrated on various test problems.

References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Zander, Nils; Bog, Tino; Kollmannsberger, Stefan; Schillinger, Dominik; Rank, Ernst: Multi-level $hp$-adaptivity: high-order mesh adaptivity without the difficulties of constraining hanging nodes (2015)
  2. Czarny, Olivier; Huysmans, Guido: Bézier surfaces and finite elements for MHD simulations (2008)
  3. Pardo, D.; Demkowicz, L.: Integration of $hp$-adaptivity and a two-grid solver for elliptic problems (2006)
  4. Rachowicz, W.; Pardo, D.; Demkowicz, L.: Fully automatic $hp$-adaptivity in three dimensions (2006)
  5. Walsh, Timothy; Demkowicz, Leszek: $hp$ boundary element modeling of the external human auditory system -- goal-oriented adaptivity with multiple load vectors. (2003)
  6. Demkowicz, L.; Bajer, A.: Conservative discretization of contact/impact problems for nearly rigid bodies (2001)
  7. Melenk, J.M.; Gerdes, K.; Schwab, Ch.: Fully discrete $hp$-finite elements: Fast quadrature (2001)
  8. Werder, T.; Gerdes, K.; Schötzau, Dominik; Schwab, Christoph: $hp$-discontinuous Galerkin time stepping for parabolic problems (2001)
  9. Demkowicz, L.; Monk, P.; Vardapetyan, L.; Rachowicz, W.: de Rham diagram for $hp$ finite element spaces (2000)
  10. Rachowicz, W.; Demkowicz, L.: An $hp$-adaptive finite element method for electromagnetics. I: Data structure and constrained approximation (2000)
  11. Schwab, Christoph; Suri, Manil: Mixed $hp$ finite element methods for Stokes and non-Newtonian flow (1999)
  12. Demkowicz, L.; Gerdes, K.; Schwab, C.; Bajer, A.; Walsh, T.: HP90: A general and flexible Fortran 90 $hp$-FE code (1998)
  13. Gerdes, K.: A summary of infinite element formulations for exterior Helmholtz problems (1998)
  14. Jacob, B.; Dragan, V.; Pritchard, A.J.: Infinite dimensional time-varying systems with nonlinear output feedback (1995)