A mixed finite element method for the stokes problem: an acceleration-pressure formulation

摘要

The existing finite element methods [6,9,11] for the Stokes equation lead to a saddle-point problem. For removing certain restrictions on the elements and improving the accuracy, this paper develops a new method: the Stokes equation is treated as a first order linear system. Using a least squares method to minimize the defect in the differential operator, we find that the result converges asymptotically to optimal order in Sobolev spaces. In the 2-D case, if the domain is subdivided into regular triangles and the piecewise linear functions in the space H1 are chosen to be trial functions for both velocity and pressure, then we have error estimates ∥p - ph∥:0 + ∥u - uh∥0 ⩽ Ch2