共查询到20条相似文献,搜索用时 0 毫秒
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Dai-quYang JenniferZhao 《计算数学(英文版)》2003,21(3):257-276
An iterative algorithm is proposed and analyzed based on a hybridized mized finite element method for numerically solving two-phase generalized Stefan interface problems with strongly discontinuous solutions,conormal derivatives,and coefficients.This algorithm iteratively solves small problems for each single phase with good accuracy and exchange information at the interface to advance the iteration until convergence ,following the idea of Schwarz Alternating Methods,Error estimates are derived to show that this algorithm always converges provided that relaxation parameters are suitably chosen,Numeric exper-iments with matching and non-matching grids at the interface from different phases are performed to show the accuracy of the method for capturing discontinuities in the solutions and coefficients.In contrast to standard numerical methods,the accuracy of our method does not seem to deteriorate as the coefficient discontinuity increases. 相似文献
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求解间断系数椭圆型问题的一种改进的DG方法 总被引:1,自引:0,他引:1
本文考虑对间断系数椭圆型问题的普通DG方法进行改进,提出了一种综合了DG方法及区域分解方法的优点的新方法.对此法进行了先验误差分析并给出其残量型后验误差估计,且通过数值实验验证了该方法及其自适应方法的有效性. 相似文献
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We derive some residual-type a posteriori error estimates for the local CO discontinuous Galerkin (LCDG) approximations ([31]) of the Kirchhoff bending plate clamped on the boundary. The estimator is both reliable and efficient with respect to the moment-field approximation error in an energy norm. Some numerical experiments are reported to demonstrate theoretical results. 相似文献
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一阶双曲问题的有限元后验误差估计至今没有得到很好的解决.本文对d维区域上一阶双曲问题的k次间断有限元逼近提出了一种新的后验误差分析方法, 进而建立了间断有限元解在DG范数下(强于L2范数)基于误差余量型的后验误差估计. 数值计算验证了本文理论分析的有效性. 本文方法也适用于其他变分问题有限元逼近的后验误差分析. 相似文献
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Ying Lungan 《数学年刊B辑(英文版)》1997,18(2):139-152
INTERFACEPROBLEMSFORELLIPTICDIFFERENTIALEQUATIONSYINGLUNGANAbstractAnewapproachisgiventoanalysetheregularityofsolutionsnears... 相似文献
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Ying Chen Jia-fu Lin Qun Lin 《计算数学(英文版)》2002,20(4):429-436
AbstractFor the first order nonstationary hyperbolic equation taking the piecewise linear discontinuous Galerkin solver, we prove that under the uniform rectangular partition, such a discontinuous solver, after postprossesing, can have two and half approximative order which is half order higher than the optimal estimate by Lesaint and Raviart under the rectangular partition. 相似文献
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In this paper, a unified model for time-dependent Maxwell equations in dispersive media is considered. The space-time DG method developed in [29] is applied to solve the underlying problem. Unconditional L2-stability and error estimate of order O τr+1+ hk+1/2 are obtained when polynomials of degree at most r and k are used for the temporal discretization and spatial discretization respectively. 2-D and 3-D numerical examples are given to validate the theoretical results. Moreover, numerical results show an ultra-convergence of order 2r + 1 in temporal variable t. 相似文献
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This paper proposes and analyzes a new weak Galerkin method for the eigenvalueproblem by using the shifted-inverse power technique. A high order lower bound canbe obtained at a relatively low cost via the proposed method. The error estimates forboth eigenvalue and eigenfunction are provided and asymptotic lower bounds are shown aswell under some conditions. Numerical examples are presented to validate the theoreticalanalysis. 相似文献
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This paper deals with the discontinuous Galerkin (DG) methods for delay differential equations.By an orthogonal analysis in each element,the superconvergence re... 相似文献
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Luca Dede 《计算数学(英文版)》2010,(1):122-148
In this work we consider the Reduced Basis method for the solution of parametrized advection-reaction partial differential equations. For the generation of the basis we adopt a stabilized finite element method and we define the Reduced Basis method in the "primal- dual" formulation for this stabilized problem. We provide a priori Reduced Basis error estimates and we discuss the effects of the finite element approximation on the Reduced Basis error. We propose an adaptive algorithm, based on the a posteriori Reduced Basis error estimate, for the selection of the sample sets upon which the basis are built; the idea leading this algorithm is the minimization of the computational costs associated with the solution of the Reduced Basis problem. Numerical tests demonstrate the efficiency, in terms of computational costs, of the "primal-dual" Reduced Basis approach with respect to an "only primal" one. Parametrized advection-reaction partial differential equations, Reduced Basis method, "primal-dual" reduced basis approach, Stabilized finite element method, a posteriori error estimation. 相似文献