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In numerical analysis, the mixed finite element method, also known as the hybrid finite element method, is a type of finite element method in which extra independent variables are introduced as nodal variables during the discretization of a partial differential equation problem. The extra independent variables are constrained by using Lagrange multipliers. To be distinguished from the mixed finite element method, usual finite element methods that do not introduce such extra independent variables are also called irreducible 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.
References

Olek C Zienkiewicz, Robert L Taylor and J.Z. Zhu. The Finite Element Method: Its Basis and Fundamentals. Elsevier.

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