论文信息 - A multiscale formulation of the Discontinuous Petrov–Galerkin method for advective–diffusive problems

A multiscale formulation of the Discontinuous Petrov–Galerkin method for advective–diffusive problems

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

[1] T. Hughes,et al. The variational multiscale method—a paradigm for computational mechanics , 1998 .

[2] Thomas J. R. Hughes,et al. The Continuous Galerkin Method Is Locally Conservative , 2000 .

[3] D. Arnold,et al. Discontinuous Galerkin Methods for Elliptic Problems , 2000 .

[4] Lutz Tobiska,et al. Numerical Methods for Singularly Perturbed Differential Equations , 1996 .

[5] Paola Causin,et al. A Discontinuous Petrov-Galerkin Method with Lagrangian Multipliers for Second Order Elliptic Problems , 2005, SIAM J. Numer. Anal..

[6] Franco Brezzi,et al. Recent results in the treatment of subgrid scales , 2002 .

[7] C. Bottasso. A new look at finite elements in time: a variational interpretation of Runge-Kutta methods , 1997 .

[8] C. Bottasso,et al. The discontinuous Petrov–Galerkin method for elliptic problems , 2002 .