Approximation of Elliptic Boundary-Value Problems
Courier Corporation, 1 janv. 2007 - 356 pages
Mathematically self-contained, this text for advanced undergraduates and graduate students combines two important methods -- the finite element method and the variational method -- into the framework of functional analysis. It does so in order to explain potential applications to approximation of nonhomogeneous boundary-value problems for elliptic operators. 1980 edition.
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approximate the solution bilinear form a(u boundary-value problem bounded open subset canonical isometry closed subspace compact support continuous and dense continuous bilinear form converges weakly COROLLARY criterion of m-convergence deﬁned Deﬁnition denote Dirichlet problem discrete error discrete norm discrete space discrete variational equation duality pairing E V(A elliptic equivalent error function exists a constant exists a unique external ﬁnite ﬁnite-element approximations ﬁrst function with compact Galerkin approximations Green formula Hilbert space implies inequality inner product internal approximation isometry isomorphism kernel Lemma Let us assume Let us consider matrix multi-integers Neumann problem number of levels obtain partial approximations phuh phvh piecewise-polynomial approximations prolongation ph quasi-optimal restriction sh satisﬁes the criterion Section smooth bounded open Sobolev spaces solution uh space H space of order stability functions Theorem 1-2 transpose unique solution V-elliptic