Mixed and hybrid finite elements methods
Research on non-standard finite element methods is evolving rapidly and in this text Brezzi and Fortin give a general framework in which the development is taking place. The presentation is built around a few classic examples: Dirichlet's problem, Stokes problem, Linear elasticity. The authors provide with this publication an analysis of the methods in order to understand their properties as thoroughly as possible.
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Variational Formulations and Finite Element Methods
Approximation of Saddle Point Problems
Function Spaces and Finite Element Approximations
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analysis apply approximation barycenter bilinear form boundary bubble functions Chapter choice CIARLET coercive computational consider continuous convergence decomposition defined degrees of freedom denote Dirichlet problem discrete problem divergence-free dual space easy to check equation equivalent error estimates Example exists Figure finite element methods fvdx G Vh Green's formula H(div Hence Hl(Q Hq(Q hybrid methods implies incompressible independent of h inf-sup condition instance interfaces introduce Jn Jn Ker Bh KerB Lagrange multiplier Lemma linear linear elasticity macroelement matrix mesh mixed methods Mk(K Moreover Neumann problem nonconforming nonconforming methods norm notation obtain optimal penalty method piecewise constant polynomials present Proof Proposition II.2.8 qh dx quadrilaterals Remark saddle point problem satisfies the inf-sup Section Sobolev spaces solve space standard Stokes problem subspace surjective Theorem triangle unique solution velocity Vg G