The Finite Element Method for Elliptic Problems

a₁ abstract error estimate analysis approximate bilinear forms assume assumption BABUŠKA basis functions bilinear form boundary value problem Bramble-Hilbert lemma Céa's lemma CIARLET constant C independent convergence convex corresponding deduce defined definition degrees of freedom denote dim PK Dirichlet problem discrete problem discrete solution equations exists a constant finite element method finite element space formula fv dx given Green's formula inclusion independent of h inequality interpolation KETH Lax-Milgram lemma lemma linear Lipschitz-continuous mapping F n-simplex n-simplices of type nodes nonconforming norm obtain P₁(K polynomial polynomials of degree proof quadrature scheme RAVIART rectangle satisfies Section semi-norms Sobolev spaces space Pk space Vn space Xh subset subspace Theorem triangle of type unique V₁ vector Vn-elliptic X₁ Zienkiewicz Δυ θη μη Σκ Φη ψη Ω Ω