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gradient recovery-Type a Posteriori Error Estimates for Steady-State Poisson-Nernst-Planck Equations

Advances in Applied Mathematics and Mechanics 2020年第6期12卷 1353-1383页

作者： Ruigang Shen Shi Shu Ying Yang Mingjuan Fang School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtanHunan 411105China School of Mathematics and Computational Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic TechnologyGuilinGuangxi 541004China School of Mathematics and Computational Science Guilin University of Electronic TechnologyGuilinGuangxi 541004China

In this article,we derive the a posteriori error estimators for a class of steadystate Poisson-Nernst-Planck *** the gradient recovery operator,the upper and lower bounds of the a posteriori error estimators are established both for the electrostatic potential and *** is shown by theory and numerical experiments that the error estimators are reliable and the associated adaptive computation is efficient for the steady-state PNP systems.

关键词： Poisson-Nernst-Planck equations gradient recovery a posteriori error estimate

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SomeWeighted Averaging Methods for gradient recovery

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Advances in Applied Mathematics and Mechanics 2012年第2期4卷 131-155页

作者： Yunqing Huang Kai Jiang Nianyu Yi Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105HunanChina

We propose some new weighted averaging methods for gradient recovery,and present analytical and numerical investigation on the performance of these weighted averaging *** is shown analytically that the harmonic averaging yields a superconvergent gradient for any mesh in one-dimension and the rectangular mesh in *** results indicate that these new weighted averaging methods are better recovered gradient approaches than the simple averaging and geometry averaging methods under triangular mesh.

关键词： Finite element method weighted averaging gradient recovery

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POLYNOMIAL PRESERVING recovery FOR ANISOTROPIC AND IRREGULAR GRIDS

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Journal of Computational Mathematics 2004年第2期22卷 331-340页

作者： ZhiminZhang DepartmentofMathematics WayneStateUniversityDetroitMI48202USA

Some properties of a newly developed polynomial preserving gradient recovery technique are discussed. Both practical and theoretical issues are addressed. Bounded-ness property is considered especially under anisotropic grids. For even-order finite element space, an ultra-convergence property is established under translation invariant meshes; for linear element, a superconvergence result is proven for unstructured grids generated by the Delaunay triangulation.

关键词： Finite element Superconvergence gradient recovery A posteriori error estimate

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Retrieving Topological Information of Implicitly Represented Diffuse Interfaces with Adaptive Finite Element Discretization

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Communications in Computational Physics 2013年第5期13卷 1209-1226页

作者： Jian Zhang Qiang Du Supercomputing center Chinese Academy of SciencesBeijingP.R.China Department of Mathematics Pennsylvania State UniversityUniversity ParkPA 16802USA State Key Laboratory of Space Weather Chinese Academy of SciencesBeijingP.R.China

We consider the finite element based computation of topological quantities of implicitly represented surfaces within a diffuse interface *** an adaptive finite element implementation with effective gradient recovery techniques,we discuss how the Euler number can be accurately computed directly from the numerically solved phase field functions or order *** examples and applications to the topological analysis of point clouds are also presented.

关键词： Diffuse interface model phase field method Euler number Gauss curvature adaptive finite element gradient recovery

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