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31.
Mohan K. Kadalbajoo Puneet Arora 《Numerical Methods for Partial Differential Equations》2010,26(5):1206-1223
The advection‐diffusion equation has a long history as a benchmark for numerical methods. Taylor‐Galerkin methods are used together with the type of splines known as B‐splines to construct the approximation functions over the finite elements for the solution of time‐dependent advection‐diffusion problems. If advection dominates over diffusion, the numerical solution is difficult especially if boundary layers are to be resolved. Known test problems have been studied to demonstrate the accuracy of the method. Numerical results show the behavior of the method with emphasis on treatment of boundary conditions. Taylor‐Galerkin methods have been constructed by using both linear and quadratic B‐spline shape functions. Results shown by the method are found to be in good agreement with the exact solution. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
32.
L. Jones Tarcius Doss A. K. Pani S. Padhy 《Numerical Methods for Partial Differential Equations》1997,13(4):393-416
Based on a Landau-type transformation, both continuous and discrete in time L2-Galerkin methods are applied to a single-phase Stefan-type problem in one space dimension. Optimal rates of convergence in Lℵ, L∞, and H1-norms are derived and computational results are presented. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 393–416, 1997 相似文献
33.
讨论了常微分方程初值问题的k次平均间断有限元.当k为偶数时,证明了在节点上的平均通量(间断有限元在节点上的左右极限的平均值)有2k+2阶最佳强超收敛性.对具有动量守恒的非线性Hamilton系统(如Schrdinger方程和Kepler系统),发现此类间断有限元在节点上是动量守恒的.这些性质被数值试验所证实. 相似文献
34.
Hassan Khosravian‐Arab Mehdi Dehghan M. R. Eslahchi 《Mathematical Methods in the Applied Sciences》2017,40(18):6389-6410
This paper presents 2 new classes of the Bessel functions on a compact domain [0,T] as generalized‐tempered Bessel functions of the first‐ and second‐kind which are denoted by GTBFs‐1 and GTBFs‐2. Two special cases corresponding to the GTBFs‐1 and GTBFs‐2 are considered. We first prove that these functions are as the solutions of 2 linear differential operators and then show that these operators are self‐adjoint on suitable domains. Some interesting properties of these sets of functions such as orthogonality, completeness, fractional derivatives and integrals, recursive relations, asymptotic formulas, and so on are proved in detail. Finally, these functions are performed to approximate some functions and also to solve 3 practical differential equations of fractionalorders. 相似文献
35.
In this article, we derive error estimates for the semi-discrete and fully discrete Galerkin approximations of a general linear second-order hyperbolic partial differential equation with general damping (which includes boundary damping). The results can be applied to a variety of cases (e.g. vibrating systems of linked elastic bodies). The results generalize pioneering work of Dupont and complement a recent article by Basson and Van Rensburg. 相似文献
36.
Le Thi Phuong Ngoc Nguyen Anh Triet Alain Pham Ngoc Dinh 《Numerical Functional Analysis & Optimization》2017,38(9):1173-1207
In this paper, we consider a wave equation with integral nonlocal boundary conditions of memory type. First, we establish two local existence theorems by using Faedo–Galerkin method and standard arguments of density. Next, we give a su?cient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results. 相似文献
37.
38.
Tuğba Akman 《Applicable analysis》2017,96(3):461-482
In this study, proper orthogonal decomposition (POD) method is applied to diffusion–convection–reaction equation, which is discretized using space–time discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and space–time projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence rates, are presented. 相似文献
39.
Ernst P. Stephan 《Applicable analysis》2013,92(1-4):59-74
A boundary integral method is developed for the mixed boundary value problem for the vector Helmholtz equation in R3. The obtained boundary integral equations for the unknown Cauchy data build a strong elliptic system of pseudodifferential equations which can therefore be used for numerical computations using Galerkin's procedure. We show existence, uniqueness and regularity of the solution of the integral equations. Especially we give the local "edge" behavior of the solution near the submanifold which divides the Dirichlet boundary from the Neumann boundary 相似文献
40.
Joachim Gwinner 《Optimization》2018,67(7):1017-1030
AbstractThis paper is concerned with elliptic variational inequalities that depend on two parameters. First, we investigate the dependence of the solution of the forward problem on these parameters and prove a Lipschitz estimate. Then, we study the inverse problem of identification of these two parameters and formulate two optimization approaches to this parameter identification problem. We extend the output least-squares approach, provide an existence result and establish a convergence result for finite-dimensional approximation. Further, we investigate the modified output least-squares approach which is based on energy functionals. This latter approach can be related to vector approximation. 相似文献