A NOTE ON THE LAX-MILGRAM THEOREM AND THE C(E)A THEOREM

摘要

This paper investigates Galerkin methods for an abstract variational problem when its bilinear form has no eoereivity,and by the use of funetional analysis theory,proves such a result:the variational problem has a unique solution and the solution can be approximated by their Galerkin approximation solutions if and only if the Galerkin approximation problems sarisfy certain stability,where the Galerkin approximation problems are supposed to have unique solutions.This result may be viewed as replenishment for the Lax-Milgram theorem and the Céa theorem;it is applied to the variational problem with or without coercivity.

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