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偏微分方程数值计算
  • 项目名称：偏微分方程数值计算
  • 项目类别：海外或港、澳青年学者合作研究基金
  • 批准号：10528102
  • 申请代码：A011701
  • 项目来源：国家自然科学基金
  • 研究期限：2006-01-01-2008-12-31
  • 项目负责人：许进超
  • 负责人职称：教授
  • 依托单位：北京大学
  • 批准年度：2005
中文摘要：

许进超教授在多层网格法和区域分解法领域取得了一系列开创性成果，为该领域的奠基人之一。其代表性的成果有1)以他和合作者名字(Bramble-Pasciak-Xu)命名的"BPX多层网格预条件子"算法; 2)"基于空间分解与子空间校正的迭代法"的理论框架;3) 原创性的二重网格法（将求解非对称或非线性问题的复杂性本质性的降低为求解简单的对称正定问题）; 4) 与Zikatanov给出的"收敛速度的恒等式"，彻底解决了"基于空间分解与子空间校正的迭代法"的收敛理论问题;5) 给出了许多基本的代数多层网格法和相关理论，包括与Zikatanov给出的基于能量极小意义的最优代数多层网格法;6) 与Randy Bank提出了一种全新的后验误差估计法，对一大类问题得到了渐近精确的误差估计式；7）与陈龙给出了一系列的非各向同性误差估计和相关的自适应算法，已被成功应用于燃料电池模型、非牛顿流体的数值模拟。

中文主题词：
成果综合统计
成果类型
数量
  • 期刊论文
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期刊论文
OPTIMAL ERROR ESTIMATES FOR NEDELEC EDGE ELEMENTS FOR TIME-HARMONIC MAXWELL'S EQUATIONS
Convergence and optimality of adaptive mixed finite element methods
Superconvergence for quadratic triangular finite elements on mildly structured grids
Uniformly-Stable Finite Element Methods for Darcy-Stokes-Brinkman Models
Convergence of adaptive Morley-type element methods
Some n-Rectangle Nonconforming Elements for Fourth Order Elliptic Equations
Local and Parallel Finite Element Algorithms for the Stokes Problem
Asymptotically Optimal and Linear-time Algorithm for Polygonal Curve Simplification
The Morley element for fourth order elliptic equations in any dimensions
Optimal anisotropic simplicial meshes for minimizing interpolation errors in ${L}^p$-norm
Nonconforming tetrahedral finite elements for fourth order elliptic equations
The finite element approximation of the nonlinear Poisson-Boltzmann equation
Modified Morley element method for a fourth elliptic singular perturbation problem
Superconvergent derivative recovery for Lagrange triangular elements of degree p on unstructured gri
A New Class of Zienkiewicz-Type Non-conforming Element in Any Dimensions
Convergence and optimal complexity of adaptive finite element eigenvalue computations
New estimates for the rate of the method of subspace corrections
A Two-grid Method of a Mixed Stokes-Darcy Model for Coupling Fluid Flow with Porous Media Flow
Nodal Auxiliary Space Preconditioning in H(curl) and H(div) spaces
A toy model for testing finite element methods to simulate extreme-mass-ration binary systems
New formulations, positivity preserving discretizations and stability analysis for non-Newtonian flo
On the well posedness of mathematical model for Lithium-Ion battery systems
Stability and accuracy of adapted finite element methods for singularly perturbed problems
Extending the applicability of multigrid methods
Auxiliary space preconditioning for edge elements
A new adaptive local mesh refinement algorithm and its application on fourth order thin film flow pr
Convergence analysis on iterative methods for semidefinite systems
Uniform convergent multigrid methods for elliptic problems with strongly discontinuous coefficients
A POSTERIORI ERROR ESTIMATES OF A NON-CONFORMING FINITE ELEMENT METHOD FOR PROBLEMS WITH ARTIFICIAL BOUNDARY CONDITIONS
CONVERGENCE ANALYSIS ON ITERATIVE METHODS FOR SEMIDEFINITE SYSTEMS
许进超的项目