Superconvergent biquadratic finite volume element method for two-dimensional Poisson's equations

Tongke Wang, Yuesheng Gu
2010 Journal of Computational and Applied Mathematics  
MSC: 65N12 65N15 Keywords: Poisson's equation Biquadratic finite volume element method Alternating direction method Optimal stress point Error estimate Superconvergence a b s t r a c t In this paper, a kind of biquadratic finite volume element method is presented for two-dimensional Poisson's equations by restricting the optimal stress points of biquadratic interpolation as the vertices of control volumes. The method can be effectively implemented by alternating direction technique. It is
more » ... that the method has optimal energy norm error estimates. The superconvergence of numerical gradients at optimal stress points is discussed and it is proved that the method has also superconvergence displacement at nodal points by a modified dual argument technique. Finally, a numerical example verifies the theoretical results and illustrates the effectiveness of the method.
doi:10.1016/j.cam.2009.12.036 fatcat:eoipnca37jecbfmaq2y6l2xnh4