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

Mathematica Applicanda (1983)

- Volume: 11, Issue: 23
- ISSN: 1730-2668

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topAdam Zemła. "Galerkin's method of variable directions for parabolic obstacle variational inequalities." Mathematica Applicanda 11.23 (1983): null. <http://eudml.org/doc/293243>.

@article{AdamZemła1983,

abstract = {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."},

author = {Adam Zemła},

journal = {Mathematica Applicanda},

keywords = {Methods of Newton-Raphson, Galerkin and Ritz types; Variational inequalities; Finite elements, Rayleigh-Ritz, Galerkin and collocation methods},

language = {eng},

number = {23},

pages = {null},

title = {Galerkin's method of variable directions for parabolic obstacle variational inequalities},

url = {http://eudml.org/doc/293243},

volume = {11},

year = {1983},

}

TY - JOUR

AU - Adam Zemła

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

JO - Mathematica Applicanda

PY - 1983

VL - 11

IS - 23

SP - null

AB - 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."

LA - eng

KW - Methods of Newton-Raphson, Galerkin and Ritz types; Variational inequalities; Finite elements, Rayleigh-Ritz, Galerkin and collocation methods

UR - http://eudml.org/doc/293243

ER -

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