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We prove the existence and nonexistence of elliptic curves having good reduction everywhere over certain real quadratic fields Q(m) for m≤200. These results of computations give best-possible data inc...
In this paper we present a numerical method for solving Riemann type problem for the fifth order improperly elliptic equation in complex plane .We reduce this problem to the boundary value problems fo...
Numerical experiments are given to verify the theoretical results for superconvergence of the elliptic problem by global and local L2-Projection methods.
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...
We propose a condition under which the heterogeneous multiscale 痭ite element method converges for elliptic problem with nonsmooth coe眂ients, and obtain the optimal convergence rate for elliptic prob...
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...
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...
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 ...
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...
The finite element solutions of elliptic eigenvalue equations are shown to have a multi-parameter asymptotic error expansion. Based on this expansion and a splitting extrapolation technique, a paral...
We develop and analyze a first-order system least-squares spectral method for the second-order elliptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted nor...
This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of bound...
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...
In this paper, some effective cascadic multigrid methods are proposed for solving the large scale symmetric or nonsymmetric algebraic systems arising from the finite volume methods for second order e...

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