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In this paper, some novel discrete formulations for stabilizing the mixed finite element method \textit{Q1-Q0} (bilinear velocity and constant pressure approximations) are introduced and discussed for the generalized Stokes problem. These are based on stabilizing discontinuous pressure approximations via local jump operators. The developing idea consists in a reduction of terms in the local jump formulation, introduced earlier, in such a way that stability and convergence properties are preserved. The computer implementation aspects and numerical evaluation of these stabilized discrete formulations are also considered. For illustrating the numerical performance of the proposed approaches and comparing the three versions of the local jump methods alongside with the global jump setting, some obtained results for two test generalized Stokes problems are presented. Numerical tests confirm the stability and accuracy characteristics of the resulting approximations.
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참고문헌 (22)
참고문헌 신청
M. Ainsworth / 2015 / Stabilization of high aspect ratio mixed nite elements for incompressible ow / SIAM J. Numer. Anal 53(2):1107~1120
J. M. Boland / 1984 / On the stability of bilinear-constant velocity-pressure nite elements / Numer. Math 44(2):219~222
J. M. Boland / 1985 / Stable and semistable low order nite elements for viscous ows / SIAM J. Numer. Anal 22(3):474~492
F. Brezzi / 1984 / On the stabilization of nite element approximations of the Stokes equations, in Ecient solutions of elliptic systems / Notes Numer. Fluid Mech 10:11~19
E. Burman / 2007 / A unied stabilized method for Stokes' and Darcy's equations / J. Comput. Appl. Math 198(1):35~51
J. M. Boland / 1984 / On the stability of bilinear-constant velocity-pressure nite elements / Numer. Math 44(2):219~222
J. M. Boland / 1985 / Stable and semistable low order nite elements for viscous ows / SIAM J. Numer. Anal 22(3):474~492
F. Brezzi / 1984 / On the stabilization of nite element approximations of the Stokes equations, in Ecient solutions of elliptic systems / Notes Numer. Fluid Mech 10:11~19
E. Burman / 2007 / A unied stabilized method for Stokes' and Darcy's equations / J. Comput. Appl. Math 198(1):35~51
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