Abstract
We study a hybridizable discontinuous Galerkin method for solving the vorticity-velocity formulation of the Stokes equations in three-space dimensions. We show how to hybridize the method to avoid the construction of the divergence-free approximate velocity spaces, recover an approximation for the pressure and implement the method efficiently. We prove that, when all the unknowns use polynomials of degree k≥0, the L 2 norm of the errors in the approximate vorticity and pressure converge with order k+1/2 and the error in the approximate velocity converges with order k+1. We achieve this by letting the normal stabilization function go to infinity in the error estimates previously obtained for a hybridizable discontinuous Galerkin method.
Original language | English (US) |
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Pages (from-to) | 256-270 |
Number of pages | 15 |
Journal | Journal of Scientific Computing |
Volume | 52 |
Issue number | 1 |
DOIs | |
State | Published - Jul 2012 |
Bibliographical note
Funding Information:The first author was partially supported by the National Science Foundation (Grant DMS-0712955) and by the Minnesota Supercomputing Institute.
Keywords
- Discontinuous Galerkin methods
- Hybridization
- Incompressible fluid flow