Application of h-, p-, and hp -Mesh Adaptation Techniques to the SP 3 Equations

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.