共查询到20条相似文献,搜索用时 815 毫秒
1.
B. Bialecki M. Ganesh K. Mustapha 《Numerical Methods for Partial Differential Equations》2005,21(5):918-937
We propose and analyze an application of a fully discrete C2 spline quadrature Petrov‐Galerkin method for spatial discretization of semi‐linear parabolic initial‐boundary value problems on rectangular domains. We prove second order in time and optimal order H1 norm convergence in space for the extrapolated Crank‐Nicolson quadrature Petrov‐Galerkin scheme. We demonstrate numerically both L2 and H1 norm optimal order convergence of the scheme even if the nonlinear source term is not smooth. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005. 相似文献
2.
四阶椭圆方程解之极值原理最先由Dunninger,D.R.提出.Goyal,V.B.和Singl,K.P.推广到半线性方程的情形,文献[5]、[6]作进一步的推广,都对文献[3]的某些结论作了修正,并且都建立四阶椭圆方程边值问题解的存在性定理。关于四阶抛物方程解的极值原理及唯一性定理作者作过讨论。这篇短文研究四阶非线性抛物方程的初值问题和混合问题解的存在性,其前提是所有解的最大模有一致先验的上界。 相似文献
3.
Tianliang Hou 《Applicable analysis》2013,92(8):1655-1665
In this article, we analyse a posteriori error estimates of mixed finite element discretizations for linear parabolic equations. The space discretization is done using the order λ?≥?1 Raviart–Thomas mixed finite elements, whereas the time discretization is based on discontinuous Galerkin (DG) methods (r?≥?1). Using the duality argument, we derive a posteriori l ∞(L 2) error estimates for the scalar function, assuming that only the underlying mesh is static. 相似文献
4.
Ranjan Kumar Mohanty 《Numerical Algorithms》2010,54(3):379-393
In this paper, the use of N-AGE and Newton-N-AGE iterative methods on a variable mesh for the solution of one dimensional
parabolic initial boundary value problems is considered. Using three spatial grid points, a two level implicit formula based
on Numerov type discretization is discussed. The local truncation error of the method is of O(k2hl-1 +khl +hl3)O({k^2h_l^{-1} +kh_l +h_l^3}), where h
l
> 0 and k > 0 are the step lengths in space and time directions, respectively. We use a special technique to handle singular parabolic
equations. The advantage of using these algorithms is highlighted computationally. 相似文献
5.
Belkacem Said-Houari 《Applicable analysis》2013,92(2):424-440
In this article, we investigate the decay properties of the linear thermoelastic plate equations in the whole space for both Fourier and Cattaneo's laws of heat conduction. We point out that while the paradox of infinite propagation speed inherent in Fourier's law is removed by changing to the Cattaneo law, the latter always leads to a loss of regularity of the solution. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We prove the decay estimates for initial data U 0?∈?H s (?)?∩?L 1(?). In addition, by restricting the initial data to U 0?∈?H s (?)?∩?L 1,γ(?) and γ?∈?[0,?1], we can derive faster decay estimates with the decay rate improvement by a factor of t ?γ/2. 相似文献
6.
Máté Matolcsi 《Acta Mathematica Hungarica》2005,108(1-2):129-136
Summary He present work deals with estimations of the n-th linear polarization constant c(H)n of an n-dimensional real Hilbert space H. We provide some new lower bounds on the value of sup║y║=1 │1,y> ... n,y>│, where x1, ... ,xn are unit vectors in H. In particular, the results improve an earlier estimate of Marcus. However, the intriguing conjecture c(H) n= nn/2 remains open. 相似文献
7.
Manuel Valdivia 《Mathematische Nachrichten》1996,181(1):277-287
Let X be a Banach space. Let Hw*(X*) the Fréchet space whose elements are the holomorphic functions defined on X* whose restrictions to each multiple mB(X*), m = 1,2, …, of the closed unit ball B(X*) of X* are continuous for the weak-star topology. A fundamental system of norms for this space is the supremum of the absolute value of each element of Hw*(X*) in mB(X*), m = 1,2,…. In this paper we construct the bidual of l1 when this space contains no copy of l1. We also show that if X is an Asplund space, then Hw*(X*) can be represented as the projective limit of a sequence of Banach spaces that are Asplund. 相似文献
8.
Ryan I. Fernandes Graeme Fairweather 《Numerical Methods for Partial Differential Equations》1993,9(2):191-211
While alternating direction implicit (ADI) collocation methods have been used for several years to solve parabolic problems in several space variables, no convergence analysis has been derived for any of these methods. We formulate and rigorously analyze ADI collocation schemes applied to the inhomogeneous heat and wave equations on the unit square subject to homogeneous Dirichlet boundary conditions and appropriate initial conditions. We prove that each method is second-order accurate in time and of optimal accuracy in space in the L2 and H01 norms. Numerical experiments confirm the predicted rates of convergence. © 1993 John Wiley & Sons, Inc. 相似文献
9.
We derive new a priori error estimates for linear parabolic equations with discontinuous coefficients. Due to low global regularity of the solutions the error analysis of the standard finite element method for parabolic problems is difficult to adopt for parabolic interface problems. A finite element procedure is, therefore, proposed and analyzed in this paper. We are able to show that the standard energy technique of finite element method for non-interface parabolic problems can be extended to parabolic interface problems if we allow interface triangles to be curved triangles. Optimal pointwise-in-time error estimates in the L 2(Ω) and H 1(Ω) norms are shown to hold for the semidiscrete scheme. A fully discrete scheme based on backward Euler method is analyzed and pointwise-in-time error estimates are derived. The interfaces are assumed to be arbitrary shape but smooth for our purpose. 相似文献
10.
Veli B. SHAKHMUROV 《数学年刊B辑(英文版)》2008,29(1):95-112
This study focuses on the anisotropic Besov-Lions type spaces B^lp,θ(Ω;E0,E) associated with Banach spaces E0 and E. Under certain conditions, depending on l =(l1,l2,…,ln)and α=(α1,α2,…,αn),the most regular class of interpolation space Eα between E0 and E are found so that the mixed differential operators D^α are bounded and compact, from B^l+s p,θ(Ω;E0,E) to B^s p,θ(Ω;Eα).These results are applied to concrete vector-valued function spaces and to anisotropic differential-operator equations with parameters to obtain conditions that guarantee the uniform B separability with respect to these parameters. By these results the maximal B-regularity for parabolic Cauchy problem is obtained. These results are also applied to infinite systems of the quasi-elliptic partial differential equations and parabolic Cauchy problems with parameters to obtain sufficient conditions that ensure the same properties. 相似文献
11.
Paul F. X. Müller 《Israel Journal of Mathematics》1987,59(2):195-212
LetF
n be an increasing sequence of finite fields on a probability space (Ω,F
n,P) whereF denotes the σ-algebra generated by ∪F
n. ThenF
n is isomorphic to one of the following spaces:H
1(δ), ΣH
n
1
,l
l. 相似文献
12.
S. N. Kudryavtsev 《Mathematical Notes》2005,77(3-4):494-498
We describe the weak asymptotics of the behavior of the Kolmogorov, Gelfand, linear, Aleksandrov, and entropy widths of the unit ball of the space W
p
l
Hw (I
d) in the space W
q
m
(I
d).Translated from Matematicheskie Zametki, vol. 77, no. 4, 2005, pp. 535–539.Original Russian Text Copyright © 2005 by S. N. Kudryavtsev.This revised version was published online in April 2005 with a corrected issue number. 相似文献
13.
We propose and analyze a fully discrete H
1-Galerkin method with quadrature for nonlinear parabolic advection–diffusion–reaction equations that requires only linear
algebraic solvers. Our scheme applied to the special case heat equation is a fully discrete quadrature version of the least-squares
method. We prove second order convergence in time and optimal H
1 convergence in space for the computer implementable method. The results of numerical computations demonstrate optimal order
convergence of scheme in H
k
for k = 0, 1, 2.
Support of the Australian Research Council is gratefully acknowledged. 相似文献
14.
B. Bialecki M. Ganesh K. Mustapha 《Numerical Methods for Partial Differential Equations》2006,22(5):1052-1069
We propose and analyze a Crank–Nicolson quadrature Petrov–Galerkin (CNQPG) ‐spline method for solving semi‐linear second‐order hyperbolic initial‐boundary value problems. We prove second‐order convergence in time and optimal order H2 norm convergence in space for the CNQPG scheme that requires only linear algebraic solvers. We demonstrate numerically optimal order Hk, k = 0,1,2, norm convergence of the scheme for some test problems with smooth and nonsmooth nonlinearities. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
15.
Giuseppe Savaré 《Numerische Mathematik》1993,65(1):319-335
Summary We study the approximation of linear parabolic Cauchy problems by means of Galerkin methods in space andA -stable multistep schemes of arbitrary order in time. The error is evaluated in the norm ofL
t
2
(H
x
1
) L
t
(L
x
2
). 相似文献
16.
In this paper Hubert's M-estimator for robust linear regression is analyzed. Newton type methods for solution of the problem are defined and analyzed, and finite convergence is proved. Numerical experiments with a large number of test problems demonstrate efficiency and indicate that this kind of approach may be useful also in solving thel
1 problem. 相似文献
17.
The parabolic Bergman space is a Banach space of L
p
-solutions of some parabolic equations on the upper half-space H. We study interpolating theorem for these spaces. It is shown that if a sequence in H is δ-separated with δ sufficiently near 1, then it interpolates on parabolic Bergman spaces.
This work was supported in part by Grant-in-Aid for Scientific Research (C) No.18540168, No.18540169, and No.19540193, Japan
Society for the Promotion of Science. 相似文献
18.
N. P. Korneichuk 《Ukrainian Mathematical Journal》1996,48(9):1423-1433
We obtain new results related to the estimation of the linear widths λ
N
and λ
N
in the spacesC andL
p
for the classesH
ω (in particular, forH
α, 0<α<1).
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 48,
No. 9, pp. 1255–1264, September, 1996. 相似文献
19.
20.
Let S be a commutative inverse semigroup and let E be its subsemigroup of idempotents. In this paper we define the n-th module cohomology group of Banach algebras and we show that H2l1(E)(l1(S),l1(S)(n))\mathcal {H}^{2}_{\ell^{1}(E)}(\ell^{1}(S),\ell^{1}(S)^{(n)}) is a Banach space for every odd n∈ℕ. 相似文献