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A low order anisotropic nonconforming characteristic finite element method for a convection-dominated transport problem. (English) Zbl 1172.65059

A numerical analysis of an approximate scheme for convection-diffusion equation in a two space dimensional domain is presented. A numerical space discretization is based on a low order Crouzeix-Raviart type anisotropic nonconforming rectangular finite element. This method is applied to the convection-diffusion problem for a modified characteristic finite element scheme. For the problem of a significant convection term a nonconforming finite element method is convenient and moreover it can be parallelized in an efficient manner.
The anisotropic interpolation operator combined with the mean value method is used instead the elliptic projection in the proposed numerical scheme. First, the construction of the discrete problem is presented and the existence and uniqueness of the solution of the discrete problem are proved. Then the error estimates in \(L_\infty([0,T],L_2(\Omega))\) of order \(O(h^2) +O(\Delta t)\) are proved. The results improve the previous error estimate of Guo and Chen. Finally numerical example with computational results and experimental order of convergence for proposed scheme is included in the paper. Numerical experiments confirm the theoretical result of the paper.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
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