Mixed finite element method

In numerical analysis, a mixed finite element method, is a variant of the finite element method in which extra fields to be solved are introduced during the posing a partial differential equation problem. Somewhat related is the hybrid finite element method. The extra fields may be constrained by using Lagrange multiplier fields. To be distinguished from the mixed finite element method, the more typical finite element methods that do not introduce such extra fields are also called irreducible or primal finite element methods.^[1] The mixed finite element method is efficient for some problems that would be numerically ill-posed if discretized by using the irreducible finite element method; one example of such problems is to compute the stress and strain fields in an almost incompressible elastic body.