A posteriori error estimation for nonlinear variational problems by duality theory. (English) Zbl 0904.65064

Repin, S. I.

J. Math. Sci., New York 99, No. 1, 927-935 (2000); translation from Zap. Nauchn. Semin. POMI 243, 201-214 (1997).

Summary: We use duality theory of the calculus of variations for deriving a posteriori error estimates. We obtain a general form of this (duality) error estimate and show that known classes of a posteriori error estimates are its particular cases.

MSC:

65K10	Numerical optimization and variational techniques
49J27	Existence theories for problems in abstract spaces
49N15	Duality theory (optimization)

Keywords:

nonlinear variational problems; Banach space; duality theory; error estimates

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