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

Adam Zemła

Mathematica Applicanda (1983)

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

Abstract

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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."

How to cite

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Adam 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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