Mixed‐hybrid finite elements and streamline computation for the potential flow problem

Abstract

Abstract An important class of problems in mathematical physics involves equations of the form −∇ · (A∇ϕ) = f . In a variety of problems it is desirable to obtain an accurate approximation of the flow quantity u = −A∇ϕ. Such an accurate approximation can be determined by the mixed finite element method. In this article the lowest‐order mixed method is discussed in detail. The mixed finite element method results in a large system of linear equations with an indefinite coefficient matrix. This drawback can be circumvented by the hybridization technique, which leads to a symmetric positive‐definite system. This system can be solved efficiently by the preconditioned conjugate gradient method. After approximating u by the lowest‐order mixed finite element method, streamlines and residence times can be determined easily and accurately by computations at the element level.