共查询到20条相似文献,搜索用时 31 毫秒
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罗振东 《数学物理学报(A辑)》2006,26(6):906-916
该文讨论平面弹性力学问题的混合元法的泡函数稳定性,并导出基于简化的稳定化格式的一种先验误差估计和后验误差估计.这种简化的稳定化格式较通常的格式节省自由度. 相似文献
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In this article, a reduced mixed finite element (MFE) formulation based on proper orthogonal decomposition (POD) for the non-stationary conduction-convection problems is presented. Also the error estimates between the reduced MFE solutions based on POD and usual MFE solutions are derived. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced MFE formulation based on POD is feasible and efficient in finding numerical solutions for the non-stationary conduction-convection problems. 相似文献
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In this paper a mixed finite element (MFE) formulation is proposed for the initial-boundary value problem of dissipative symmetric regularized long wave (SRLW) equations with damping. Existence and uniqueness of its generalized solution and of the fully discrete mixed finite element solution are proved. Error estimates based on energy methods are given. Numerical experiments verify the theoretical analysis. 相似文献
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Based on the primal mixed variational formulation, a stabilized nonconforming mixed finite element method is proposed for the linear elasticity on rectangular and cubic meshes. Two kinds of penalty terms are introduced in the stabilized mixed formulation, which are the jump penalty term for the displacement and the divergence penalty term for the stress. We use the classical nonconforming rectangular and cubic elements for the displacement and the discontinuous piecewise polynomial space for the stress, where the discrete space for stress are carefully chosen to guarantee the well-posedness of discrete formulation. The stabilized mixed method is locking-free. The optimal convergence order is derived in the $L^2$-norm for stress and in the broken $H^1$-norm and $L^2$-norm for displacement. A numerical test is carried out to verify the optimal convergence of the stabilized method. 相似文献
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非粘性土壤中溶质运移问题的守恒混合有限元法及其数值模拟 总被引:2,自引:1,他引:1
奉文建立了非粘性土壤水中溶质运移问题的守恒混合元格式,讨论了广义解和混合元解的存在唯一性,并给出了误差估计.数值模拟结果表叫,用该方法模拟溶质运移问题是合理有效的,不仅提高了通量的模拟精度,而且使计算稳定. 相似文献
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The moving finite element (MFE) method, when applied to purelyhyperbolic partial differential equation, moves nodes with approximatelycharacteristic speeds, which makes the method useless for steady-stateproblems. We introduce the least squares MFE method (LSMFE)for steady-state pure convection problems which corrects thisdefect. We show results for a steady-state pure convection problemin one dimension in which the nodes are no longer swept downstreamas in MFE. The method is then extended to two dimensions andthe grid aligns automatically with the flow, thereby yieldingfar greater accuracy than the corresponding fixed node leastsquares results, as is shown in two-dimensional numerical trials. 相似文献
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Silvia Bertoluzza 《Numerische Mathematik》2000,86(1):1-28
Summary. We propose here a stabilization strategy for the Lagrange multiplier formulation of Dirichlet problems. The stabilization
is based on the use of equivalent scalar products for the spaces and , which are realized by means of wavelet functions. The resulting stabilized bilinear form is coercive with respect to the
natural norm associated to the problem. A uniformly coercive approximation of the stabilized bilinear form is constructed
for a wide class of approximation spaces, for which an optimal error estimate is provided. Finally, a formulation is presented
which is obtained by eliminating the multiplier by static condensation. This formulation is closely related to the Nitsche's method for solving Dirichlet boundary value problems.
Received December 4, 1998 / Revised version received May 7, 1999 / Published online April 20, 2000 –? Springer-Verlag 2000 相似文献
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S. Bertoluzza 《Applied Mathematics Letters》1998,11(6):129-134
We take advantage of the results of norm characterization by multiscale decomposition to introduce a stabilized formulation of an abstract noncoercive problem. The resulting stabilized problem is positive definite and can therefore be safely discretized by the Galerkin method. 相似文献
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In this study, a time semi-discrete Crank-Nicolson (CN) formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite element (SCNMFE) formulation based on two local Gauss integrals and parameterfree with the second-order time accuracy is established directly from the time semi-discrete CN formulation. Thus, it could avoid the discussion for semi-discrete SCNMFE formulation with respect to spatial variables and its theoretical analysis becomes very simple. Finaly, the error estimates of SCNMFE solutions are provided. 相似文献
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M. J. Baines 《Numerical Methods for Partial Differential Equations》1994,10(2):191-203
It is shown that, for a class of time-dependent partial differential equations of the form ut = ??u, one step of the moving finite-element (MFE) procedure corresponds to one iteration of an algorithm for obtaining best L2 fits with adjustable nodes to continuous functions. In the steady-state limit the MFE procedure gives the best fit of ??u, with adjustable nodes, to the null function. For first-order partial differential equations, the MFE procedure moves nodes with approximate characteristic nodal speeds. We identify an additional speed component arising directly from the L2 projection which seeks a best fit in the sense described above. © 1994 John Wiley & Sons, Inc. 相似文献
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《数学物理学报(B辑英文版)》2015,(5)
A time semi-discrete Crank-Nicolson(CN) formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established.And then, a fully discrete stabilized CN mixed finite volume element(SCNMFVE) formulation based on two local Gaussian integrals and parameter-free with the second-order time accuracy is established directly from the time semi-discrete CN formulation so that it could avoid the discussion for semi-discrete SCNMFVE formulation with respect to spatial variables and its theoretical analysis becomes very simple. Finally, the error estimates of SCNMFVE solutions are provided. 相似文献