Temat: Rayleigh - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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

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Skocz do pozycji: 2.

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

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Skocz do pozycji: 3.

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

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Skocz do pozycji: 4.

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

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Skocz do pozycji: 5.

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

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