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Mathematics of Computation

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A stable, direct solver for the gradient equation

Author: Rob Stevenson
Journal: Math. Comp. 72 (2003), 41-53
MSC (2000): Primary 65N30, 65F05, 42C40, 76D05, 35Q30
Published electronically: June 6, 2002
MathSciNet review: 1933813
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Abstract: A new finite element discretization of the equation $\mathbf{grad}\,p =\mathbf{g}$ is introduced. This discretization gives rise to an invertible system that can be solved directly, requiring a number of operations proportional to the number of unknowns. We prove an optimal error estimate, and furthermore show that the method is stable with respect to perturbations of the right-hand side $\mathbf{g}$. We discuss a number of applications related to the Stokes equations.

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Additional Information

Rob Stevenson
Affiliation: Department of Mathematics, Utrecht University, P.O. Box 80.010, NL-3508 TA Utrecht, The Netherlands

Keywords: LBB-stability, Stokes equations, multiscale bases, direct solver
Received by editor(s): April 28, 1998
Published electronically: June 6, 2002
Article copyright: © Copyright 2002 American Mathematical Society