Application of h-, p-, and hp-Mesh Adaptation Techniques to the SP₃ Equations

Abstract

This paper is devoted to the application of isotropic and anisotropic mesh adaptivity techniques to the SP ₃ equations. We compare uniform refinements, h-, p-, and hp-adaptivity techniques. h-versions only refine the mesh cells whereas p-versions increase locally the polynomial order of the approximation. hp-adaptivity combines both techniques but requires more knowledge regarding the shape of the error. The hp-finite element method (hp-FEM) generates a sequence of adapted meshes by either performing h- or p-refinements, based upon which choice is locally more efficient. At each adaptivity step, a pair of coarse/fine adapted meshes is employed to compute the local error and to determine the next adapted mesh that best minimizes the projection-based interpolation error. The implementation of the various hp-strategies analyzed is performed with the hp-FEM Hermes2D code and numerical results are presented for the SP ₃ equations.

Keywords:

• Adaptive mesh refinement
• SP ₃ equations
• hp-adaptivity

Acknowledgement

The author acknowledges financial support from the US Department of Energy Nuclear Energy University Programs (under BEA contract No. 0008911, subcontract UNR–10-32) for this work.