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A multiscale formulation of the discontinuous Petrov-Galerkin method for advective-diffusive problems. (English) Zbl 1093.76030

Summary: We consider the discontinuous Petrov-Galerkin method for the advection-diffusion model problem, and we investigate the application of variational multiscale method to this formulation. We show the exact modeling of fine scale modes at the element level for the linear case, and we discuss the approximate modeling both in the linear and nonlinear cases. Furthermore, we highlight the existing link between this multiscale formulation and \(p\)-version of finite element method. Numerical examples illustrate the behavior of the proposed scheme.

MSC:

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