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Superconvergence effect in finite element methods for two-point boundary value problems

100%

Regińska T.

Mathematica Applicanda

1987

tom 16

nr 30

Approximate methods for solving two-point boundary value problems are considered. The aim of the paper is to explain superconvergence effect in the methods using finite element spaces. The existence of a class of the methods with the superconvergence property is demonstrated. Detailed proofs of superconvergence are presented for the case of the Galerkin method (due to Douglas and Dupont results) and for some example of external method.

Galerkin's method of variable directions for parabolic obstacle variational inequalities

80%

Zemła A.

Mathematica Applicanda

1983

tom 11

nr 23

Author introduction (translated from the Polish): "This paper is an attempt to extend Galerkin's variable directions method ADG, used in the solution of differential equations [see M. Dryja , same journal 15 (1979), 5–23; MR0549983; G. Fairweather , Finite element Galerkin methods for differential equations, Chapter 6, Dekker, New York, 1978; MR0495013] to inequalities. The numerical properties of the scheme of the ADG method are discussed using the example of the following variational problem: Find a function u:(0,T)→K⊂V⊂H such that: (u′+Au−f,v−u)H≥0 for all v∈K and almost all t in [0,T), u(0)=u0, where V and H are Hilbert spaces of functions defined on Ω. The problem studied in this paper is called a parabolic obstacle variational inequality. We restrict ourselves to problems with a symmetric operator A whose coefficients do not depend on the time variable."

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2 Mathematica Applicanda

1 Regińska T.

1 Zemła A.

1 1987

1 1983

Wyniki wyszukiwania

Superconvergence effect in finite element methods for two-point boundary value problems

Galerkin's method of variable directions for parabolic obstacle variational inequalities