A quadratic finite volume element method for parabolic problems on quadrilateral meshes

In this paper we utilize affine biquadratic elements and a two-step temporal discretization to develop a finite volume element method for parabolic problems on quadrilateral meshes. The method is proved to have an optimal order convergence rate in L2(0,T; H1(Ω)) under the ‘asymptotically parallelogram’ mesh assumption. Numerical experiments that corroborate the theoretical analysis are also presented.

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