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Wyszukujesz frazę "Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods" wg kryterium: Temat

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    Wyświetlanie 1-7 z 7
    Tytuł:
    Alternating direction Galerkin method for quasilinear parabolic equations
    Autorzy:
    Dryja, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/748658.pdf
    Data publikacji:
    1979
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
    Opis:
    MR0549983
    Consider the following parabolic equation: (1) ∂u/∂t−∑2i=1(d/dxi)ai(x,t,u,D1u,D2u)+a0(x,t,u,D1u,D2u)=f(x,t), x=(x1,x2)∈Ω⊂R2, t∈[0,T], with the initial value condition u(x,0)=u0(x), x∈Ω, and with the boundary value condition u(x,t)=0, x∈∂Ω, t∈[0,T]. For the solution of equation (1) the author proposes a variational-difference method. Namely, he approximates equation (1) by Galerkin's method with respect to the variables x1,x2 and by the finite-difference method with respect to the variable t. Under some assumptions concerning the coefficients ai, i=0,1,2, an estimate of the error is given.
    Źródło:
    Mathematica Applicanda; 1979, 7, 15
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Superconvergence in the finite element method
    Autorzy:
    Leyk, Zbigniew
    Powiązania:
    https://bibliotekanauki.pl/articles/748740.pdf
    Data publikacji:
    1982
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
    Opis:
    MR0707821
    For some variants of the finite element method there exist points having a remainder value or a derivation remainder remarkably less than those given by global norms. This phenomenon is called superconvergence and the points are called superconvergence points. The generalized problem corresponding to (1) is as follows: Let Hk(Ω) be Sobolev space and Hk0(Ω) the completion of the space C∞0(Ω) with norm ∥⋅∥k,Ω. Find u∈H10(Ω) such that for each v∈H10(Ω), (2) a(u,v)=(f,v)0 holds, where a(u,v)=∫Ω(∑n|α|=0aα(x)DαuDαv)dx, (f,v)0=∫Ωf(x)v(x)dx, Dα=Dα11⋯Dαnn,1.5pt Dαiiu=∂αiu/∂xαii, i=1,n¯¯¯¯¯¯¯¯. The approximate problem of the finite element variant considered is the following: Find uh∈Vh such that (3) for all v∈Vh, a(uh,v)=(f,v)0. The main result is the theorem: Let ai∈C(Ω¯), D1ai,D2ai∈L∞(Ω),i=1,2,∥σ∥∞L(Ω)≤σ,f∈L2(Ω). Suppose the eigenvalues of the operator L are different from zero, and u∈H4(Ω)∩H10(Ω). Then there exists h0 such that for h≤h0, h2∑P∈G|grad(u−uh)(P)|≤Ch3(|u|3+|u|4), where u and uh are the solutions of problems (2) and (3), respectively, and C is some constant independent of h. Further, |u|k={∫Ω(∑|α|=k(Dαu)2)dx}1/2, G=⋃N1N2i=1Fi(R), R={(±3√/3,±3√/3)} is a Gauss point set in the quadrant S={(ξ1,ξ2):|ξk|≤1,k=1,2}, and Fi(F(1)i,F(2)i):S→ei, ei an element; F(1)i(ξ1,ξ2)=x(i)0+h1ξ1/2, F(2)i(ξ1,ξ2)=y(i)0+h2ξ2/2, and (x(i)0,y(i)0) is the middle element.
    Źródło:
    Mathematica Applicanda; 1982, 10, 20
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The projective-Newton methods
    Autorzy:
    Hobot, Grażyna
    Pokora, Teresa
    Powiązania:
    https://bibliotekanauki.pl/articles/748356.pdf
    Data publikacji:
    1986
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
    Single equations
    Opis:
    .
    In this paper we consider the Newton-like methods for the solution of nonlinear equations. In each step of the Newton method the linear equations are solved approximatively by a projection method. We call this a projective-Newton method. We investigate the convergence and the order of convergence for these methods. Next, the projective-Newton methods in the finite element space are applied for nonlinear elliptic boundary value problems. In this case the linear equations of the Newton method are solved by the Ritz method.
    Źródło:
    Mathematica Applicanda; 1986, 14, 27
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A method for solving the Neumann problem for the Poisson equation on the exterior of a poligon
    Autorzy:
    Roliński, Tomasz
    Powiązania:
    https://bibliotekanauki.pl/articles/747369.pdf
    Data publikacji:
    1993
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Boundary element methods
    Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
    Opis:
    .
    This paper is concerned with a numerical method for solving the problem Δu=f in Ωc (=intR2\Ω), (du/dn)|Γ=g, where ΩR2 is a polygon and Γ is the boundary of Ω. The method is based on coupling finite and boundary element techniques. To compensate for the loss of smoothness of the solution u near the corners of the polygon Ω we refine the triangulation without changing the number of triangles. We apply the affine triangular Lagrangean element of degree kN and the Lagrangean boundary element of degree k−1 to obtain the optimal order of convergence via the Galerkin projection.
    Źródło:
    Mathematica Applicanda; 1993, 22, 36
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An analysis of the exterior Neumann problem for the Poisson equation in connection with a numerical procedure
    Autorzy:
    Roliński, Tomasz
    Powiązania:
    https://bibliotekanauki.pl/articles/747373.pdf
    Data publikacji:
    1993
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Boundary element methods
    Boundary value problems for second-order elliptic equations
    Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
    Opis:
    .
    This paper is concerned with transforming the exterior problem Δu=f on Ωc, (∂u/∂n)|Γ=g, where ΩR2 is a bounded region and Ω^(c)=int(R2\Ω), into a problem represented by two equations. The first one is posed on a bounded domain and the second one is posed on the outer part of the boundary of the domain. This new problem is suitable for a numerical method based on coupling the finite and boundary element methods.
    Źródło:
    Mathematica Applicanda; 1993, 22, 36
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Galerkins method of variable directions for parabolic obstacle variational inequalities
    Autorzy:
    Zemła, Adam
    Powiązania:
    https://bibliotekanauki.pl/articles/747741.pdf
    Data publikacji:
    1983
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Methods of Newton-Raphson, Galerkin and Ritz types
    Variational inequalities
    Finite elements, Rayleigh-Ritz, Galerkin and collocation methods
    Opis:
    .
    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."
    Źródło:
    Mathematica Applicanda; 1983, 11, 23
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Superconvergence effect in finite element methods for two-point boundary value problems
    Autorzy:
    Regińska, Teresa
    Powiązania:
    https://bibliotekanauki.pl/articles/747715.pdf
    Data publikacji:
    1987
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Boundary value problems
    Finite elements, Rayleigh-Ritz, Galerkin and collocation methods
    Opis:
    .
    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.
    Źródło:
    Mathematica Applicanda; 1987, 16, 30
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-7 z 7

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