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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A posteriori error estimate for a WG method of H(curl)-elliptic problems
H（卷曲） 椭圆问题 WG方法 后验误差估计
2023/4/23
In this paper, a posteriori error estimate of a weak Galerkin (WG) finite element method for solving H(curl)-elliptic problems is designed and analyzed. Firstly, a WG method for H(curl)-elliptic probl...
A fast direct solver for elliptic problems on general meshes in 2D
Elliptic equations Fast algorithms Multifrontal methods Hierarchical matrices Sparse matrix
2015/7/14
We present a fast direct algorithm for solutions to linear systems arising from 2D elliptic equations. We follow the approach in Xia et al. (2009) on combining the multifrontal method with hierarchica...
A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices
Elliptic equations Fast algorithms Nested dissection Hierarchical matrices Sparse matrix
2015/7/14
We present a fast algorithm for solutions to linear systems arising from three dimensional elliptic problems on a regular Cartesian mesh. We follow the approach of Schmitz and Ying (2012) on combining...
An Efficient High Order Heterogeneous Multiscale Method For Elliptic Problems
Heterogeneous multiscale method H-convergence Least-squares
2012/8/10
We propose an efficient heterogeneous multiscale finite element
method based on a local least-squares reconstruction of the effective matrix
using the data retrieved from the solution of cell proble...
Nonoverlapping Domain Decomposition Methods with Simplified Coarse Spaces for Solving Three-dimensional Elliptic Problems
domain decomposition coarse subspace substructuring preconditioner inexact solver condition number
2012/8/8
In this paper we propose a substructuring preconditioner for solving three-dimensional
elliptic equations with strongly discontinuous coe±cients. The new preconditioner
can be viewed as a variant of...
Global compactness for a class of quasi-linear elliptic problems
Quasi-linear equations global compactness of Palais-Smale sequences
2011/9/15
Abstract: We prove a global compactness result for Palais-Smale sequences associated with a class of quasi-linear elliptic equations on exterior domains.
Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients
Multigrid Preconditioner Elliptic Problems Jump Coefficients Numerical Analysis
2011/9/1
Abstract: In this paper, we present a multigrid preconditioner for solving the linear system arising from the piecewise linear nonconforming Crouzeix-Raviart discretization of second order elliptic pr...
Weak Optimal Controls in Coefficients for Linear Elliptic Problems
degenerate elliptic equations control in coefficients
2011/2/21
In this paper we study an optimal control problem associated to a linear degenerate elliptic equation with mixed boundary conditions. The equations of this type can exhibit the Lavrentieff phenomenon ...
Multilevel Preconditioners for Discontinuous Galerkin Approximations of Elliptic Problems with Jump Coefficients
Multilevel preconditioner discontinuous Galerkin methods Crouzeix-Raviart nite elements
2011/1/19
In this article we develop and analyze two-level and multi-level methods for the
family of Interior Penalty (IP) discontinuous Galerkin (DG) discretizations of second order
elliptic problems with ro...
Coincidence sets in quasilinear elliptic problems of monostable type
Coincidence sets quasilinear elliptic problems of monostable type
2010/12/7
This paper concerns the formation of a coincidence set for the positive solution of the boundary value problem: −"pu = uq−1 f (a(x)−u) in with u = 0 on @ , where " is a positive pa...
A PARALLEL ITERATIVE DOMAIN DECOMPOSITION ALGORITHM FOR ELLIPTIC PROBLEMS
Domain decomposition methods finite element methods parallel computing
2007/12/12
An iterative nonoverlapping domain decomposition procedure is proposed
and analyzed for linear elliptic problems. At the interface of two
subdomains, one subdomain problem requires that Dirichlet da...
Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios
multiscale elliptic problems domain decomposition
2007/12/11
In this paper we study some nonoverlapping domain decomposition methods for solving a class of elliptic problems arising from composite materials and flows in porous media which contain many spatial s...
On the Boundary Behaviour, Including Second Order Effects, of Solutions to Singular Elliptic Problems
elliptic problems singular equations boundary behaviour
2007/12/11
For $\gamma\ge 1$ we consider the solution $u=u(x)$ of the Dirichlet boundary value problem $\Delta u+u^{-\gamma}=0$ in $\Omega$, $u=0$ on $\partial\Omega$. For $\gamma=1$ we find the estimate $$u(x)=...
The Ritz projections of the elliptic problem-\partial_i (a_(ij)(\partial _ju)+c_0u=f in Ω, u=0 on \partial Ω,and the quasilinear eiliptic problem-\partial (a_i(x,Du))+a_0(x,Du)=0 in Ω, u=0 on \partial...
We present an overview of the recent development on numerical methods for elliptic problems with multiscale coecients. We carry out a thorough study of two representative techniques: the heterogeneou...