Hermite finite elements for second order boundary value problems with sharp gradient discontinuities

• Autores: Vitoriano Ruas
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 246, Nº 1, 2013, págs. 234-242
• Idioma: inglés
• DOI: 10.1016/j.cam.2012.08.027
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• Resumen

  • In two recent papers the author introduced a finite element method to solve second order elliptic equations in N-dimensional space, for N = 2 and N = 3 respectively, providing flux continuity across inter-element boundaries on the basis of Hermite interpolation in an N-simplex. After defining this method in the framework of diffusion-like problems with anisotropic diffusion tensors, another N-simplex based Hermite finite element method to solve the same class of problems is considered. The latter can be viewed as a variant of the popular lowest-order Raviart�Thomas mixed element known as RT0. A convergence analysis of this method is given, showing that, in contrast to RT0, it is second order accurate in L2. Some numerical examples comparing the three methods are given.