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High accuracy analysis of the characteristic-nonconforming FEM for a convection-dominated transport problem. (English) Zbl 1293.65131

A low-order characteristic-nonconforming \(EQ_1^{\mathrm{rot}}\) finite element method (FEM) is proposed for solving a two-dimensional convection-dominated transport problem. On the basis of the distinguish property of the \(EQ_1^{\mathrm{rot}}\) element, that is, the consistency error can be estimated as order \(\mathcal O(h^2)\), the authors futher study by using a fine error estimate techniques the superclose and superconvergence results in broken energy norm, which make up the shortage of previous literature. Lastly, some numerical results are provided to verify their theoretical analysis.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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