Nonconforming P1 Finite Element for the Biharmonic Problem and Its Application to Stokes Problem.

The aim of this paper is to simulate the two-dimensional stationary Stokes problem. In vorticity-Stream function formulation, the Stokes problem is reduced to a biharmonic one; this approach leads to a formulation only based on the stream functions and therefore can only be applied to two-dimensional problems. The idea developed in this paper is to use the discretization of the Laplace operator by the nonconforming P 1 finite element. For the solutions which admit a regularity greater than H 0 2 (Ω) , in the general case, the convergence of the method is shown with the techniques of compactness. For solutions in C 4 (Ω ̄) , an error estimate is proved, and numerical experiments are performed for the steady-driven cavity problem. [ABSTRACT FROM AUTHOR]