论文信息 - Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.)

Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.)

Abstract The equivalence between stabilized finite element methods (or Galerkin-least-squares tyoe methods, Ga.l.s.) and the standard Galerkin method with bubble functions is established in an abstract framework. The results are applicable to various finite element spaces, including high order elements, and applications to the advective diffusive model and to the Stokes problem are presented, illustrating the potential of the abstract theory introduced here.

[1] L. Franca,et al. Error analysis of some Galerkin least squares methods for the elasticity equations , 1991 .

[2] J. Douglas,et al. Stabilized mixed methods for the Stokes problem , 1988 .

[3] F. Brezzi,et al. A relationship between stabilized finite element methods and the Galerkin method with bubble functions , 1992 .

[4] Roger Pierre,et al. Simple C o approximations for the computation of incompressible flows , 1988 .

[5] M. Fortin,et al. A stable finite element for the stokes equations , 1984 .

[6] T. Hughes,et al. Two classes of mixed finite element methods , 1988 .

[7] T. Hughes,et al. Stabilized finite element methods. I: Application to the advective-diffusive model , 1992 .

[8] T. Hughes,et al. A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuscka-Brezzi condition: A stable Petrov-Galerkin formulation of , 1986 .

[9] Claes Johnson. Numerical solution of partial differential equations by the finite element method , 1988 .

[10] Thomas J. R. Hughes,et al. The Stokes problem with various well-posed boundary conditions - Symmetric formulations that converge for all velocity/pressure spaces , 1987 .

[11] Jim Douglas,et al. An absolutely stabilized finite element method for the stokes problem , 1989 .