Elliptic Problems: Approximation by Mixed and Hybrid Methods
In this Chapter, we consider some alternative formulations of second order linear elliptic equations, based on variational principles that differ from the classical one presented in the previous Chapter. We then introduce new numerical approaches that are tailored on the new formulations. More precisely, we first introduce the so-called equilibrium finite element methods through the minimization of the complementary energy. We then consider the Hellinger-Reissner principle, giving rise to both mixed and hybrid finite element methods. Finally, a more general analysis of saddle-point problems and their approximation via Lagrangian multipliers is provided.
KeywordsBilinear Form Hybrid Method Elliptic Problem Compatibility Condition Neumann Problem
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