Abstract
In this paper, we introduce and analyze local discontinuous Galerkin methods for the Stokes system. For a class of shape regular meshes with hanging nodes we derive a priori estimates for the L2-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 ≥ 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.
Original language | English (US) |
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Pages (from-to) | 319-343 |
Number of pages | 25 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 40 |
Issue number | 1 |
DOIs | |
State | Published - Apr 2002 |
Keywords
- Discontinuous Galerkin methods
- Finite elements
- Stokes system