Abstract
A modified mixed/hybrid finite element method, which is no longer reguired to satisfy the Babuska-Brezzi condition, is referred to as a stabilized method. Based on the duality of variational principles in solid mechanics, a new type of stabilized method, called the combinatorially stabilized mixed/hybrid finite element method, is presented by weight-averaging both the primal and the dual “saddle-point” schemes. Through a general analysis of stability and convergence under an abstract framework, it is shown that for the methods only an inf-sup inequality much weaker than Babuska-Brezzi condition needs to be satisfied. As a concrete application, it is concluded that the combinatorially stabilized Raviart and Thomas mixed methods permit theC (0)-elements to replace theH(div; Ω)-elements.
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