An absolutely stabilized finite element method for the Stokes problem

Douglas, Jim; Wang, Jun Ping

doi:10.1090/S0025-5718-1989-0958871-X

An absolutely stabilized finite element method for the Stokes problem
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by Jim Douglas and Jun Ping Wang PDF

Math. Comp. 52 (1989), 495-508 Request permission

Abstract:

An absolutely stabilized finite element formulation for the Stokes problem is presented in this paper. This new formulation, which is nonsymmetric but stable without employment of any stability constant, can be regarded as a modification of the formulation proposed recently by Hughes and Franca in [8]. Optimal error estimates in ${L^2}$-norm for the new stabilized finite element approximation of both the velocity and the pressure fields are established, as well as one in ${H^1}$-norm for the velocity field.

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