The Finite Element Method for Elliptic Problems

a₁ abstract error estimate affine family analysis approximate bilinear forms assume assumption BABUŠKA basis functions Bibliography and Comments bilinear form boundary value problem Bramble-Hilbert lemma Céa's lemma CIARLET Comput consider constant C independent convergence convex corresponding deduce defined definition degrees of freedom denote dim Pk Dirichlet problem discrete problem discrete solution equations Exercise exists a constant finite element method finite element space formulation given GLOWINSKI Green's formula H¹(N H²(N inclusion independent of h inequality KEJh L²(N Lax-Milgram lemma lemma linear Lipschitz-continuous mapping F minimization problem n-simplex n-simplices of type nodes nonconforming norm obtain P₁(K polynomial polynomials of degree prove quadrature scheme RAVIART satisfies Section semi-norms Sobolev spaces space PK subset subspace triangles of type unique V-elliptic V₁ variational problem vector vertices Zienkiewicz