Actas de congresos
Two-dimensional H(div)-conforming Finite Element Spaces With Hp-adaptivity
Registro en:
978-3-319-39929-4; 978-3-319-39927-0
Numerical Mathematics And Advanced Applications . Springer Int Publishing Ag, v. 112, p. 87 - 94, 2016.
1439-7358
WOS:000398020000009
10.1007/978-3-319-39929-4_9
Autor
Devloo
Philippe R. B.; Farias
Agnaldo M.; Gomes
Sonia M.; de Siqueira
Denise
Institución
Resumen
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) The purpose of the paper is to analyse the effect of hp mesh adaptation when discretized versions of finite elementmixed formulations are applied to elliptic problems with singular solutions. Two stable configurations of approximation spaces, based on affine triangular and quadrilateral meshes, are considered for primal and dual (flux) variables. When computing sufficiently smooth solutions using regular meshes, the first configuration gives optimal convergence rates of identical approximation orders for both variables, as well as for the divergence of the flux. For the second configuration, higher convergence rates are obtained for the primal variable. Furthermore, after static condensation is applied, the condensed systems to be solved have the same dimension in both configuration cases, which is proportional to their border flux dimensions. A test problem with a steep interior layer is simulated, and the results demonstrate exponential rates of convergence. Comparison of the results obtained with H-1-conforming formulation are also presented. 112 87 94 CNPq - the Brazilian Research Council CAPES Foundation, within the Ministry of Education in Brazil Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) Sep 14-18, 2015 Middle E Tech Univ, Inst Appl Math, Ankara, TURKEY