共查询到20条相似文献,搜索用时 15 毫秒
1.
We study an ODE‐based iterative method, the residual velocity method, for steady state free boundary problems. The convergence analysis of the method, as well as the numerical implementation based on Euler's method were provided by Donaldson and Wetton (J Appl Math 71 (2006), 877–897). In this article, we develop an enhanced Euler's method which is nearly as simple as the modified Euler's method but can achieve a rapid convergence rate similar to the fourth‐order Runge‐Kutta method. Numerical results are also provided to verify the validity of our method. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012 相似文献
2.
Mahmoudreza Bazarganzadeh Farid Bozorgnia 《Numerical Methods for Partial Differential Equations》2013,29(5):1709-1728
In this work, we present two numerical schemes for a free boundary problem that is called one phase quadrature domain. In the first method, using the properties of a given free boundary problem, we derive a method that leads us to a fast iterative solver. The iteration procedure is adapted to work in the case when topology changes. The second method is based on shape reconstruction to establish an efficient shape Quasi‐Newton method. Various numerical experiments confirm the efficiency of the derived numerical methods. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
3.
易法槐 《应用数学学报(英文版)》1998,14(1):48-57
1.IntroductionSuperconductorsofTypeIarematerialswhicharecapableofchangingfromthephaseofbeingnormalconductorstoaphasewherethereisnoresistancetothemotionoffreeelections.InnormalconductorphasethenormalizedMaxwellequations(neglectingdisplacementcurrents)aretogetherwithOhm'slawj~acEwhereuistheelectricconductivity.InasuperconductingphaseOhm'slawisnolongervalidandMaxwell'sequationsaresupplemelltedbytheGinzburg-Landaufieldequationsll].Underisothermalconditions,thechangeofphasefromsuperconductingto… 相似文献
4.
Dong Liang Hong Wang Robert C. Sharpley 《Numerical Methods for Partial Differential Equations》2006,22(6):1267-1288
In this article, we consider a single‐phase coupled nonlinear Stefan problem of the water‐head and concentration equations with nonlinear source and permeance terms and a Dirichlet boundary condition depending on the free‐boundary function. The problem is very important in subsurface contaminant transport and remediation, seawater intrusion and control, and many other applications. While a Landau type transformation is introduced to immobilize the free boundary, a transformation for the water‐head and concentration functions is defined to deal with the nonhomogeneous Dirichlet boundary condition, which depends on the free boundary function. An H1‐finite element method for the problem is then proposed and analyzed. The existence of the approximation solution is established, and error estimates are obtained for both the semi‐discrete schemes and the fully discrete schemes. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
5.
周富军 《高校应用数学学报(英文版)》2006,21(2):143-151
§1Introduction Avarietyofpartialdifferentialequationmodelsfortumorgrowthortherapyhave beendevelopedinthelastthreedecades[see2,3,16-18,21-26].Mostofthosemodelsare informoffreeboundaryproblems,andareverydiversified.Rigorousmathematical analysisofsuchfreeboundaryproblemshasdrawngreatinterest,andmanyinteresting resultshavebeenestablished[4-15].Inthispaperwedealwithamathematicalmodeldescribingtumorchemotherapy.In thismodelthetumorisviewedasdenselypacked,radially-symmetricsphereofradiusR(t)contain… 相似文献
6.
M. Poghosyan R. Teymurazyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2009,44(3):192-204
This paper studies a free boundary problem for the heat equation in a convex ring. It is proved that the considered problem has unique solution under some conditions on the initial data. 相似文献
7.
Grzegorz ukaszewicz Witold Sadowski 《Mathematical Methods in the Applied Sciences》2000,23(12):1023-1035
We consider a boundary value problem describing the stationary flow of a non‐Newtonian fluid through the frozen ground, with a free interface between the liquid and the solid phases. We prove the existence of at least one weak solution of the problem. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
8.
Domingo Alberto Tarzia 《Numerical Methods for Partial Differential Equations》1999,15(3):355-369
We consider a material that occupies a convex polygonal bounded domain Ω ⊂ ℝn, with regular boundary Γ = Γ1 ∪ Γ2 (with Γ ∩ Γ = ∅︁) with meas (Γ1) = |Γ1| > 0 and |Γ2| > 0. We assume, without loss of generality, that the melting temperature is 0°C. We consider the following steady‐state heat conduction problem in Ω: with α, q, B = Const > 0, and q and α represent the heat flux on Γ2 and the heat transfer coefficient on Γ1, respectively. In a previous article (Tabacman‐ Tarzia, J Diff Eq 77 (1989), 16– 37) sufficient and/or necessary conditions on data α, q, B, Ω, Γ1, Γ2 to obtain a temperature u of nonconstant sign in Ω (that is, a multidimensional steady‐state, two‐phase, Stefan problem) were studied. In this article, we consider a regular triangulation by finite element method of the domain Ω with Lagrange triangles of the type 1, with h > 0 the parameter of the discretization. We study sufficient (and/or necessary) conditions on data α, q, B, Ω, Γ1, and Γ2 to obtain a change of phase (steady‐state, two‐phase, discretized Stefan problem) in corresponding discretized domain, that is, a discrete temperature of nonconstant sign in Ω. Moreover, error bounds as a function of the parameter h, are also obtained. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq. 15: 355–369, 1999 相似文献
9.
TANGWEIJUN 《高校应用数学学报(英文版)》1997,12(4):427-440
In this paper, a new method of boundary reduction is proposed, which reduces thesteady-state heat transfer equation with radiation. Moreover, a boundary element method is pre-sented for its solution and the error estimates of the numerical approximations are given. 相似文献
10.
AbstractWe consider almost minimizers to the one-phase energy functional and we prove their optimal Lipschitz regularity and partial regularity of their free boundary. These results were recently obtained by David and Toro, and David, Engelstein, and Toro. Our proofs provide a different method based on a non-infinitesimal notion of viscosity solutions that we introduced. 相似文献
11.
12.
研究了乳腺癌的早期生长模型(DCIS),它为耦合了抛物方程、椭圆方程的自由边界问题,运用椭圆型方程的变分理论、抛物方程的L^p理论和压缩映照原理,证明了这个问题局部解的存在惟一性,然后用延拓方法得到了整体解的存在惟一性。 相似文献
13.
Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions 总被引:1,自引:0,他引:1
We formulate and analyze a Crank-Nicolson finite element Galerkin method and an algebraically-linear extrapolated Crank-Nicolson method for the numerical solution of a semilinear parabolic problem with nonlocal boundary conditions. For each method, optimal error estimates are derived in the maximum norm.Dedicated to Professor J. Crank on the occasion of his 80th birthdaySupported in part by the National Science Foundation grant CCR-9403461.Supported in part by project DGICYT PB95-0711. 相似文献
14.
A. Chakib A. Nachaoui M. Nachaoui 《Numerical Methods for Partial Differential Equations》2013,29(5):1563-1586
In this article, we deal with the approximation of an optimal shape design approach for a free boundary problem modeling a welding process. We consider discretization of this problem based on linear finite elements. We prove the existence of discrete optimal solutions. This allows us to show the convergence result of a sequence of discrete solutions to the continuous one. Finally, methods for numerical realization are described and several examples have been carried out to illustrate the efficiency of the proposed approach. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
15.
Håkan Hedenmalm 《Journal of Mathematical Analysis and Applications》2006,314(1):345-362
In practical work with American put options, it is important to be able to know when to exercise the option, and when not to do so. In computer simulation based on the standard theory of geometric Brownian motion for simulating stock price movements, this problem is fairly easy to handle for options with a short lifespan, by analyzing binomial trees. It is considerably more challenging to make the decision for American put options with long lifespan. In order to provide a satisfactory analysis, we look at the corresponding free boundary problem, and show that the free boundary—which is the curve that separates the two decisions, to exercise or not to—has an asymptotic expansion, where the coefficient of the main term is expressed as an integral in terms of the free boundary. This raises the perspective that one could use numerical simulation to approximate the integral and thus get an effective way to make correct decisions for long life options. 相似文献
16.
C. Nazaret 《Mathematical Methods in the Applied Sciences》1998,21(2):165-185
We consider the problem of a polygonal plate with free edges. It is a boundary value problem for the biharmonic operator on a polygon with Neumann boundary conditions. Its resolution is studied via boundary integral equations. A variational formulation of the boundary problem obtained by a double-layer potential is given. Finally, we implement the method and give numerical results. © 1998 B. G. Teubner Stuttgart–John Wiley & Sons Ltd. 相似文献
17.
Norikazu Saito Yoshiki Sugitani 《Numerical Methods for Partial Differential Equations》2019,35(1):181-199
Convergence results are presented for the immersed boundary (IB) method applied to a model Stokes problem. As a discretization method, we use the finite element method. First, the immersed force field is approximated using a regularized delta function. Its error in the W?1, p norm is examined for 1 ≤ p < n/(n ? 1), with n representing the space dimension. Subsequently, we consider IB discretization of the Stokes problem and examine the regularization and discretization errors separately. Consequently, error estimate of order h1 ? α in the W1, 1 × L1 norm for the velocity and pressure is derived, where α is an arbitrary small positive number. The validity of those theoretical results is confirmed from numerical examples. 相似文献
18.
19.
In this paper, we prove a uniqueness theorem for a free boundary problem which is given in the form of a variational inequality. This free boundary problem arises as the limit of an equation that serves as a basic model in population biology. Apart from the interest in the problem itself, the techniques used in this paper, which are based on the regularity theory of variational inequalities and of harmonic functions, are of independent interest, and may have other applications.
20.
Recently, Tian and Friedman et al. developed a mathematical model on brain tumour recurrence after resection [J.P. Tian, A. Friedman, J. Wang and E.A. Chiocca, Modeling the effects of resection, radiation and chemotherapy in glioblastoma, J. Neuro-Oncol. 91(3) (2009), pp. 287–293]. The model is a free boundary problem with a hyperbolic system of nonlinear partial differential equations. In this article, we conduct a rigorous analysis on this hyperbolic system and prove the local and global existence and uniqueness of the solution. It is well known that most nonlinear free boundary problems are impossible to solve in terms of explicit analytical solutions. In contrast, the free boundary problem in this study is solvable, and the explicit solution is found using the backward characteristic curve method. This explicit solution is then validated by numerical simulation results. An interesting finding in this study is that the problem can be treated as a hyperbolic system defined on an infinite domain where the initial condition has a first-type discontinuity. 相似文献