## A posteriori error estimation for variational problems with uniformly convex functionals.(English)Zbl 0949.65070

Variational problems of the form $\inf_{v\in V} (F(v)+ G(\Lambda v)),$ where $$F:V\to \mathbb{R}$$ is a convex lower semicontinuous functional, $$G: Y\to\mathbb{R}$$ is a uniformly convex functional, $$V$$ and $$Y$$ are reflexive Banach spaces and $$\Lambda: V\to Y$$ is a bounded linear operator is considered. A general scheme for deriving a posteriori error estimates by using the duality theory from the calculus of variations is introduced. It is shown that the main classes of such a posteriori estimates can be justified via the duality theory.

### MSC:

 65K10 Numerical optimization and variational techniques 49J27 Existence theories for problems in abstract spaces
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### References:

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