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How to avoid the use of Green’s theorem in the Ciarlet-Raviart theory of variational crimes. (English) Zbl 0623.65072
This paper generalizes previous work to the solution of a given variational problem where it is only assumed that \(u\in H^ 1(\Omega)\) and not that Green’s theorem can be used. The particular problem considered is of the form \(a(u,v)=L(v)\), \(v\in V\), where the space V is defined and \(u\in W=\{x\in H^ 1(\Omega)\), \(\bar x=\bar u\) on the boundary\(\}\). This problem is replaced by a discrete approximation the assumptions (or variational crimes) used being the approximations of V and W by finite spaces or manifolds, simplifications of the boundary and numerical integration techniques. The convergence and errors are discussed.
Reviewer: B.Burrows

MSC:
65K10 Numerical optimization and variational techniques
65J10 Numerical solutions to equations with linear operators (do not use 65Fxx)
49K27 Optimality conditions for problems in abstract spaces
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References:
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