Piecewise linear approach to the stokes equations in 3-D

摘要

Since the beginning of the 1970's, people have developed mixed finite element methods for incompressible flow. The velocity and pressure interpolations are required to satisfy a Ladyshenskaya-Babuska-Brezzi (LBB) condition which precludes many natural elements. Over the past 20 years, most mathematicians and engineers believed this to be necessary. In this research, a least-squares method for three-dimensional (3-D) problems is proposed. This method leads to a minimization problem and thus it is not subject to the restriction of the LBB condition. Piecewise linear elements can be applied for the approximation functions; the simplest and natural elements are easy to program and achieve optimal rates of convergence.