A stable, direct solver for the gradient equation

Stevenson, Rob

doi:10.1090/S0025-5718-02-01436-9

A stable, direct solver for the gradient equation
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by Rob Stevenson PDF

Math. Comp. 72 (2003), 41-53 Request permission

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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