Coupling of continuous and discontinuous Galerkin methods for transport problems. (English) Zbl 1101.76355

Summary: We formulate a coupled discontinuous/continuous Galerkin method for the numerical solution of convection-diffusion (transport) equations, where convection may be dominant. One motivation for this approach is to use a discontinuous method where the solution is rough, e.g., in regions of high gradients, and use a continuous method where the solution is smooth. In this approach, the domain is decomposed into two regions, and appropriate transmission conditions are applied at the interface between regions. In one region, a local discontinuous Galerkin method is applied, and in the other region a standard continuous Galerkin method is employed. Stability and a priori error estimates for the coupled method are derived, and numerical results in one space dimension are given for smooth problems and problems with sharp fronts.


76M10 Finite element methods applied to problems in fluid mechanics
76R99 Diffusion and convection
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