Discontinuous Galerkin Two-Grid Method for the Transient Navier–Stokes Equations

Author:

Ray Kallol1,Goswami Deepjyoti1,Bajpai Saumya2

Affiliation:

1. Department of Mathematical Sciences , Tezpur University , Tezpur , Sonitpur, Assam-784028 , India

2. School of Mathematics and Computer Science , Indian Institute of Technology Goa , Ponda , Goa - 403401 , India

Abstract

Abstract In this paper, we apply a two-grid scheme to the DG formulation of the 2D transient Navier–Stokes model. The two-grid algorithm consists of the following steps: Step 1 involves solving the nonlinear system on a coarse mesh with mesh size 𝐻, and Step 2 involves linearizing the nonlinear system by using the coarse grid solution on a fine mesh of mesh size ℎ and solving the resulting system to produce an approximate solution with desired accuracy. We establish optimal error estimates of the two-grid DG approximations for the velocity and pressure in energy and L 2 L^{2} -norms, respectively, for an appropriate choice of coarse and fine mesh parameters. We further discretize the two-grid DG model in time, using the backward Euler method, and derive the fully discrete error estimates. Finally, numerical results are presented to confirm the efficiency of the proposed scheme.

Funder

Council of Scientific and Industrial Research, India

Science and Engineering Research Board

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

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