共查询到20条相似文献,搜索用时 15 毫秒
1.
Ricardo Prato Torres Catalina Domínguez Stiven Díaz 《Numerical Methods for Partial Differential Equations》2019,35(1):325-348
In this article, we conduct an a posteriori error analysis of the two‐dimensional time‐dependent Stokes problem with homogeneous Dirichlet boundary conditions, which can be extended to mixed boundary conditions. We present a full time–space discretization using the discontinuous Galerkin method with polynomials of any degree in time and the ? 2 ? ?1 Taylor–Hood finite elements in space, and propose an a posteriori residual‐type error estimator. The upper bounds involve residuals, which are global in space and local in time, and an L 2‐error term evaluated on the left‐end point of time step. From the error estimate, we compute local error indicators to develop an adaptive space/time mesh refinement strategy. Numerical experiments verify our theoretical results and the proposed adaptive strategy. 相似文献
2.
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
3.
Ningning Yan 《Applications of Mathematics》2009,54(3):267-283
In this paper, we discuss the numerical simulation for a class of constrained optimal control problems governed by integral
equations. The Galerkin method is used for the approximation of the problem. A priori error estimates and a superconvergence
analysis for the approximation scheme are presented. Based on the results of the superconvergence analysis, a recovery type
a posteriori error estimator is provided, which can be used for adaptive mesh refinement.
The research project is supported by the National Basic Research Program under the Grant 2005CB321701 and the National Natural
Science Foundation of China under the Grant 10771211. 相似文献
4.
Jiachuan Zhang Jingshi Li Jingzhi Li Kai Zhang 《Numerical Methods for Partial Differential Equations》2020,36(6):1280-1303
Based on a posteriori error estimator with hierarchical bases, an adaptive weak Galerkin finite element method (WGFEM) is proposed for the elliptic problem with mixed boundary conditions. For the posteriori error estimator, we are only required to solve a linear algebraic system with diagonal entries corresponding to the degree of freedoms, which significantly reduces the computational cost. The upper and lower bounds of the error estimator are shown to addresses the reliability and efficiency of the adaptive approach. Numerical simulations are provided to demonstrate the effectiveness and robustness of the proposed method. 相似文献
5.
6.
An initial boundary value problem for a pseudoparabolic equation with a nonlinear boundary condition
Stanilslav N. Antontsev Serik E. Aitzhanov Dinara T. Zhanuzakova 《Mathematical Methods in the Applied Sciences》2023,46(1):1111-1136
An initial boundary value problem for a quasilinear equation of pseudoparabolic type with a nonlinear boundary condition of the Neumann–Dirichlet type is investigated in this work. From a physical point of view, the initial boundary value problem considered here is a mathematical model of quasistationary processes in semiconductors and magnets, which takes into account a wide variety of physical factors. Many approximate methods are suitable for finding eigenvalues and eigenfunctions in problems where the boundary conditions are linear with respect to the desired function and its derivatives. Among these methods, the Galerkin method leads to the simplest calculations. On the basis of a priori estimates, we prove a local existence theorem and uniqueness for a weak generalized solution of the initial boundary value problem for the quasilinear pseudoparabolic equation. A special place in the theory of nonlinear equations is occupied by the study of unbounded solutions, or, as they are called in another way, blow-up regimes. Nonlinear evolutionary problems admitting unbounded solutions are globally unsolvable. In the article, sufficient conditions for the blow-up of a solution in a finite time in a limited area with a nonlinear Neumann–Dirichlet boundary condition are obtained. 相似文献
7.
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
8.
S.A. Yousefi Mehdi Dehghan 《Numerical Methods for Partial Differential Equations》2009,25(6):1502-1510
An inverse problem concerning diffusion equation with a source control parameter is investigated. The approximation of the problem is based on the Legendre multiscaling basis. The properties of Legendre multiscaling functions are first presented. These properties together with Galerkin method are then utilized to reduce the inverse problem to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the new technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
9.
Fei Wang 《Numerical Methods for Partial Differential Equations》2013,29(2):706-720
In this article the ideas in Wang et al. [SIAM J Numec Anal 48 (2010), 708–73] are extended to solve the double obstacle problem using discontinuous Galerkin methods. A priori error estimates are established for these methods, which reach optimal order for linear elements. We present a test example, and the numerical results on the convergence order match the theoretical prediction. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013 相似文献
10.
We present two new mixed finite element methods coupled with a boundary method for the three dimensional magnetostatic problem. Such formulations are obtained by coupling a finite element method inside a bounded domain with a boundary integral method involving either the Calderon equations or the inverse of Dirichlet Neumann operator to treat the exterior domain. First, we present the formulations and then prove that our mixed formulations are well posed and that they lead to a convergent Galerkin method. Finally, we give numerical results for a sphere immersed in a homogeneous (source) field in the two formulations. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 443–462, 2003 相似文献
11.
An Ton Bui 《Journal of Mathematical Analysis and Applications》2006,317(1):286-301
The exact controllability of a semilinear wave equation, with Dirichlet boundary control on a part of the boundary and an unknown source, is shown. The nonlinear term has at most a linear growth, the initial and target spaces are L2(Ω)×H−1(Ω). 相似文献
12.
《Optimization》2012,61(5):707-715
In this article, we investigate the optimal control problem governed by parabolic inclusion. We describe the Galerkin approximation and we demonstrate the existence of the strong condensation points of the set of solutions of approximate optimization problems. Each of these points is a solution of the initial optimization problem. 相似文献
13.
Prof. Dr. V.A Yurko 《Results in Mathematics》1996,30(3-4):346-373
An inverse problem for operators of a triangular structure is studied. An algorithm for the solution and necessary and sufficient conditions for the solvability of this problem are obtained, moreover uniqueness is proved. Applications to difference and differential operators are considered. 相似文献
14.
A. Zaghdani 《Applied mathematics and computation》2010,217(5):1791-1810
We present two new coupling models for the three dimensional magnetostatic problem. In the first model, we propose a new coupled formulation, prove that it is well posed and solves Maxwell’s equations in the whole space. In the second, we propose a new coupled formulation for the Local Discontinuous Galerkin method, the finite element method and the boundary element method. This formulation is obtained by coupling the LDG method inside a bounded domain Ω1 with the FEM method inside a layer where Ω is a bounded domain which is made up of material of permeability μ and such that , and with a boundary element method involving Calderon’s equations. We prove that our formulation is consistent and well posed and we present some a priori error estimates for the method. 相似文献
15.
Hongsen Chen. 《Mathematics of Computation》2005,74(251):1097-1116
In this paper we derive some pointwise error estimates for the local discontinuous Galerkin (LDG) method for solving second-order elliptic problems in (). Our results show that the pointwise errors of both the vector and scalar approximations of the LDG method are of the same order as those obtained in the norm except for a logarithmic factor when the piecewise linear functions are used in the finite element spaces. Moreover, due to the weighted norms in the bounds, these pointwise error estimates indicate that when at least piecewise quadratic polynomials are used in the finite element spaces, the errors at any point depend very weakly on the true solution and its derivatives in the regions far away from . These localized error estimates are similar to those obtained for the standard conforming finite element method.
16.
In [35, 36], we presented an $h$-adaptive Runge-Kutta
discontinuous Galerkin method using troubled-cell indicators for
solving hyperbolic conservation laws. A tree data structure (binary
tree in one dimension and quadtree in two dimensions) is used to aid
storage and neighbor finding. Mesh adaptation is achieved by
refining the troubled cells and coarsening the untroubled
"children". Extensive numerical tests indicate that the proposed $h$-adaptive method is capable of saving the computational cost and
enhancing the resolution near the discontinuities. In this paper, we
apply this $h$-adaptive method to solve Hamilton-Jacobi equations,
with an objective of enhancing the resolution near the
discontinuities of the solution derivatives. One- and
two-dimensional numerical examples are shown to illustrate the
capability of the method. 相似文献
17.
18.
Erwin Hernández Dante Kalise Enrique Otárola 《Journal of Computational and Applied Mathematics》2011,235(5):1383-1393
In this paper we analyze a locking-free numerical scheme for the LQR control of a Timoshenko beam. We consider a non-conforming finite element discretization of the system dynamics and a control law constant in the spatial dimension. To solve the LQR problem we seek a feedback control which depends on the solution of an algebraic Riccati equation. An optimal error estimate for the feedback operator is proved in the framework of the approximation theory for control of infinite dimensional systems. This estimate is valid with constants that do not depend on the thickness of the beam, which leads to the conclusion that the method is locking-free. In order to assess the performance of the method, numerical tests are reported and discussed. 相似文献
19.
Consider scattering of electromagnetic waves by a doubly periodic structure with for integers , . Above the structure, the medium is assumed to be homogeneous with a constant dielectric coefficient. The medium is a perfect conductor below the structure. An inverse problem arises and may be described as follows. For a given incident plane wave, the tangential electric field is measured away from the structure, say at for some large . To what extent can one determine the location of the periodic structure that separates the dielectric medium from the conductor? In this paper, results on uniqueness and stability are established for the inverse problem. A crucial step in our proof is to obtain a lower bound for the first eigenvalue of the following problem in a convex domain :
20.
Rui Ding Quan Shen Yuebin Huo 《Numerical Methods for Partial Differential Equations》2021,37(1):69-97
This paper is proposed for the error estimates of the element‐free Galerkin method for a quasistatic contact problem with the Tresca friction. The penalty method is used to impose the clamped boundary conditions. The duality algorithm is also given to deal with the non‐differentiable term in the quasistatic contact problem with the Tresca friction. The error estimates indicate that the convergence order is dependent on the nodal spacing, the time step, the largest degree of basis functions in the moving least‐squares approximation, and the penalty factor. Numerical examples demonstrate the effectiveness of the element‐free Galerkin method and verify the theoretical analysis. 相似文献