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1.
Macro-elements of smoothness C
r
on Powell–Sabin triangle splits are constructed for all r0. These new elements are improvements on elements constructed in [13] in that certain unneeded degrees of freedom have been removed. 相似文献
2.
Hendrik Speleers Paul DierckxStefan Vandewalle 《Journal of Computational and Applied Mathematics》2007
Powell–Sabin splines are piecewise quadratic polynomials with a global C1-continuity, defined on conforming triangulations. Imposing boundary conditions on such a spline leads to a set of constraints on the spline coefficients. First, we discuss boundary conditions defined on a polygonal domain, before we treat boundary conditions on a general curved domain boundary. We consider Dirichlet and Neumann conditions, and we show that a particular choice of the PS-triangles at the boundary can greatly simplify the corresponding constraints. Finally, we consider an application where the techniques developed in this paper are used: the numerical solution of a partial differential equation by the Galerkin and collocation method. 相似文献
3.
Monica Morales Hernandez Leo G. Rebholz Cristina Tone Florentina Tone 《Numerical Methods for Partial Differential Equations》2016,32(4):1155-1183
We consider the stability of an efficient Crank–Nicolson–Adams–Bashforth method in time, finite element in space, discretization of the Leray‐α model. We prove finite‐time stability of the scheme in L2, H1, and H2, as well as the long‐time L‐stability of the scheme under a Courant‐Freidrichs‐Lewy (CFL)‐type condition. Numerical experiments are given that are in agreement with the theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1155–1183, 2016 相似文献
4.
We consider the non‐local singular boundary value problem (1) where q ∈ C0([0,1]) and f, h ∈ C0((0,∞)), limf(x)=?∞, limh(x)=∞. We present conditions guaranteeing the existence of a solution x ∈ C1([0,1]) ∩ C2((0,1]) which is positive on (0,1]. The proof of the existence result is based on regularization and sequential techniques and on a non‐linear alternative of Leray–Schauder type. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
5.
Changxing Miao Baoquan Yuan Bo Zhang 《Mathematical Methods in the Applied Sciences》2007,30(8):961-976
This paper is concerned with well‐posedness of the incompressible magneto‐hydrodynamics (MHD) system. In particular, we prove the existence of a global mild solution in BMO?1 for small data which is also unique in the space C([0, ∞); BMO?1). We also establish the existence of a local mild solution in bmo?1 for small data and its uniqueness in C([0, T); bmo?1). In establishing our results an important role is played by the continuity of the bilinear form which was proved previously by Kock and Tataru. In this paper, we give a new proof of this result by using the weighted Lp‐boundedness of the maximal function. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
6.
Xenakis Ioakim Yiorgos‐Sokratis Smyrlis 《Mathematical Methods in the Applied Sciences》2016,39(8):2159-2178
I. Stratis In this work, we investigate the analyticity properties of solutions of Kuramoto–Sivashinsky‐type equations in two spatial dimensions, with periodic initial data. In order to do this, we explore the applicability in three‐dimensional models of a spectral method, which was developed by the authors for the one‐dimensional Kuramoto–Sivashinsky equation. We introduce a criterion, which provides a sufficient condition for analyticity of a periodic function u∈C∞, involving the rate of growth of ?nu, in suitable norms, as n tends to infinity. This criterion allows us to establish spatial analyticity for the solutions of a variety of systems, including Topper–Kawahara, Frenkel–Indireshkumar, and Coward–Hall equations and their dispersively modified versions, once we assume that these systems possess global attractors. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
7.
Choonkil Park 《Mathematische Nachrichten》2008,281(3):402-411
Let X, Y be Banach modules over a C *‐algebra. We prove the Hyers–Ulam–Rassias stability of the following functional equation in Banach modules over a unital C *‐algebra: It is shown that a mapping f: X → Y satisfies the above functional equation and f (0) = 0 if and only if the mapping f: X → Y is Cauchy additive. As an application, we show that every almost linear bijection h: A → B of a unital C *‐algebra A onto a unital C *‐algebra B is a C *‐algebra isomorphism when h (2d uy) = h (2d u) h (y) for all unitaries u ∈ A, all y ∈ A, and all d ∈ Z . (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
8.
In this paper, we consider the Petrov–Galerkin spectral method for fourth‐order elliptic problems on rectangular domains subject to non‐homogeneous Dirichlet boundary conditions. We derive some sharp results on the orthogonal approximations in one and two dimensions, which play important roles in numerical solutions of higher‐order problems. By applying these results to a fourth‐order problem, we establish the H2‐error and L2‐error bounds of the Petrov–Galerkin spectral method. Numerical experiments are provided to illustrate the high accuracy of the proposed method and coincide well with the theoretical analysis. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
9.
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
10.
Shijin Ding Jinrui Huang Xiao‐e Liu Huanyao Wen 《Mathematical Methods in the Applied Sciences》2011,34(12):1499-1511
In this paper, we consider the existence of global smooth solutions to 1D compressible isentropic Navier–Stokes equations with density‐dependent viscosity and free boundaries. The initial density ρ0∈W1,2n is bounded below away from zero and the initial velocity u0∈L2n. The viscosity coefficient µ is proportional to ρθ with 0<θ?1, where ρis the density. The existence and uniqueness of global solutions in Hi([0,1])(i = 1,2,4) have been established in (J. Math. Phys. 2009; 50 :023101; Meth. Appl. Anal. 2005; 12 :239–252; J. Differ. Equations 2008; 245:3956–3973; Commun. Pure Appl. Anal. 2008; 7 :373–381). By mathematical induction method, we will establish the existence of global smooth solutions to 1D compressible isentropic Navier–Stokes equations with density‐dependent viscosity and free boundaries when the initial data ρ0 and u0 are smooth. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
11.
Takayuki Kubo 《Mathematical Methods in the Applied Sciences》2005,28(11):1341-1357
We shall construct a periodic strong solution of the Navier–Stokes equations for some periodic external force in a perturbed half‐space and an aperture domain of the dimension n?3. Our proof is based on Lp–Lq estimates of the Stokes semigroup. We apply Lp–Lq estimates to the integral equation which is transformed from the original equation. As a result, we obtain the existence and uniqueness of periodic strong solutions. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
12.
We consider the long‐time behavior and optimal decay rates of global strong solution to three‐dimensional isentropic compressible Navier–Stokes (CNS) system in the present paper. When the regular initial data also belong to some Sobolev space with l?4 and s∈[0, 1], we show that the global solution to the CNS system converges to the equilibrium state at a faster decay rate in time. In particular, the density and momentum converge to the equilibrium state at the rates (1 + t)?3/4?s/2 in the L2‐norm or (1 + t)?3/2?s/2 in the L∞‐norm, respectively, which are shown to be optimal for the CNS system. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
13.
In this paper, we study the existence of positive solutions for the following Sturm–Liouville‐like four‐point singular boundary value problem (BVP) with p‐Laplacian where ?p(s)=|s|p?2 s, p>1, f is a lower semi‐continuous function. Using the fixed‐point theorem of cone expansion and compression of norm type, the existence of positive solution and infinitely many positive solutions for Sturm–Liouville‐like singular BVP with p‐Laplacian are obtained. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
14.
We study the behaviour of moments of order p (1 < p < ∞) of affine and quadratic forms with respect to non log‐concave measures and we obtain an extension of Khinchine–Kahane inequality for new families of random vectors by using Pisier's inequalities for martingales. As a consequence, we get some estimates for the moments of affine and quadratic forms with respect to a tail volume of the unit ball of lnq (0 < q < 1). (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
We give a generalization of the Stone–Weierstrass property for subalgebras of C (X), with X a completely regular Hausdorff space. In particular, we study in this paper some subalgebras of C0(X), with X a locally compact Hausdorff space, provided with weighted norm topology. By using the Stone–Weierstrass property, we then describe the ideal structure of these algebras. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
Multiple non semi‐trivial solutions of systems of Kirchhoff‐type equations with discontinuous nonlinearities in RN
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In the present paper, we study the problem of multiple non semi‐trivial solutions for the following systems of Kirchhoff‐type equations with discontinuous nonlinearities (1.1) where F∈C1(RN×R+×R+,R),V∈C(RN,R), and By establishing a new index theory, we obtain some multiple critical point theorems on product spaces, and as applications, three multiplicity results of non semi‐trivial solutions for (1.1) are obtained. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
17.
Matthias Büger 《Mathematische Nachrichten》2001,222(1):31-78
We examine the autonomous reaction–diffusion system with Dirichlet boundary conditions on (0, 1), where α, β are real, α > 0, and g is C1 and satisfies some conditions which we need in order to prove the existence of solutions. We construct a solution of (RD) for every initial value in L2((0, 1)) × L2((0, 1)), we show that this solution is uniquely determined and that the solution has C∞–smooth representatives for all positive t. We determine the long time behaviour of each solution. In particular, we show that each solution of (RD) tends either to the zero solution or to a periodic orbit. We construct all periodic orbits and show that their number is always finite. It turns out that the global attractor is a finite union of subsets of L2 × L2, which are finite–dimensional manifolds, and the dynamics in these sets can be described completely. 相似文献
18.
We consider a two‐level block Gauss–Seidel iteration for solving systems arising from finite element discretizations employing higher‐order elements. A p‐hierarchical basis is used to induce this block structure. Using superconvergence results normally employed in the analysis of gradient recovery schemes, we argue that a massive reduction of the H1‐error occurs in the first iterate, so that the discrete solution is adequately resolved in very few iterates—sometimes a single iteration is sufficient. Numerical experiments on uniform and adapted meshes support these claims. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
19.
Cameron–Liebler line classes are sets of lines in PG(3, q) that contain a fixed number x of lines of every spread. Cameron and Liebler classified Cameron–Liebler line classes for x ∈ {0, 1, 2, q2 ? 1, q2, q2 + 1} and conjectured that no others exist. This conjecture was disproven by Drudge for q = 3 [8] and his counterexample was generalized to a counterexample for any odd q by Bruen and Drudge [4]. A counterexample for q even was found by Govaerts and Penttila [9]. Non‐existence results on Cameron–Liebler line classes were found for different values of x. In this article, we improve the non‐existence results on Cameron–Liebler line classes of Govaerts and Storme [11], for q not a prime. We prove the non‐existence of Cameron–Liebler line classes for 3 ≤ x < q/2. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 342–349, 2008 相似文献
20.
Michel Leblond 《Numerical Linear Algebra with Applications》2002,9(2):181-193
In computer graphics, in the radiosity context, a linear system Φx=b must be solved and there exists a diagonal positive matrix H such that H Φ is symmetric. In this article, we extend this property to complex matrices: we are interested in matrices which lead to Hermitian matrices under premultiplication by a Hermitian positive‐definite matrix H. We shall prove that these matrices are self‐adjoint with respect to a particular innerproduct defined on ?n. As a result, like Hermitian matrices, they have real eigenvalues and they are diagonalizable. We shall also show how to extend the Courant–Fisher theorem to this class of matrices. Finally, we shall give a new preconditioning matrix which really improves the convergence speed of the conjugate gradient method used for solving the radiosity problem. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献