## 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 49K27 Optimality conditions for problems in abstract spaces
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### References:

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