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Local discontinuous Galerkin methods for the Stokes system

by B. Cockburn and G. Kanschat and D. Schötzau and Ch. Schwab

(Report number 2000-14)

Abstract
In this paper, we introduce and analyze local discontinuous Galerkin methods for the Stokes system. For arbitrary meshes with hanging nodes and elements of various shapes we derive a priori estimates for the L^2-norm of the errors in the velocities and the pressure. We show that optimal order estimates are obtained when polynomials of degree k are used for each component of the velocity and polynomials of degree k-1 for the pressure, for any k \ge 1 . We also consider the case in which all the unknowns are approximated with polynomials of degree k and show that, although the orders of convergence remain the same, the method is more efficient. Numerical experiments verifying these facts are displayed.

Keywords: Finite elements, discontinuous Galerkin methods, Stokes system

@Techreport{CKSS00_273,
  author = {B. Cockburn and G. Kanschat and D. Sch\"otzau and Ch. Schwab},
  title = {Local discontinuous Galerkin methods for the Stokes system},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2000-14},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2000/2000-14.pdf },
  year = {2000}
}

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