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Finite Element Interpolation Theory
Finite Element Approximation of Elliptic
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affine equivalent affine maps Babuska Banach space bilinear form boundary conditions Ciarlet consider constraint construct continuously embedded degrees of freedom Dirichlet problem elliptic embedding equations error estimates example Exercise exists a constant exists a unique family of finite finding u e finite element approximation finite element methods given Green's formulas H and G H X Q Hilbert spaces Hm(Q hold hybrid finite element hybrid method independent of h inequality Lagrange multipliers Lemma linear space master element mesh mixed finite element mixed methods Neumann problem nodal points nodes norm notation Oden and Reddy P-unisolvent partition polynomials of degree Proof qh e Qh quotient space rate of convergence Raviart saddle point satisfying seminorm shown in Fig Sobolev spaces space H subdomains tions triangle u e H unique solution v e H variational boundary-value problem variational problem vector