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Characteristics weak Galerkin finite element methods for convection-dominated diffusion problems. (English) Zbl 1470.65171

Summary: The weak Galerkin finite element method is combined with the method of characteristics to treat the convection-diffusion problems on the triangular mesh. The optimal order error estimates in \(H^1\) and \(L^2\) norms are derived for the corresponding characteristics weak Galerkin finite element procedure. Numerical tests are performed and reported.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods 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
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