Journal
SIAM REVIEW
Volume 47, Issue 1, Pages 50-66Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0036144503426074
Keywords
finite elements; Neumann problem; Rayleigh-Ritz minimization; regularization; quadratic programming
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This paper considers the finite element approximation and algebraic solution of the pure Neumann problem. Our goal is to present a concise variational framework for the finite element solution of the Neumann problem that focuses on the interplay between the algebraic and variational problems. While many of the results that stem from our analysis are known by some experts, they are seldom derived in a rigorous fashion and remain part of numerical folklore. As a result, this knowledge is not accessible (or appreciated) by many practitioners-both novices and experts-in one source. Our paper contributes a simple, yet insightful link between the continuous and algebraic variational forms that will prove useful.
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