Some Current Questions on Solving Linear Elliptic Problems.
Some equilibrium and mixed models in the finite element method
Some Equilibrium Finite Element Methods for Two- Dimensional Elasticity Problems.
Some fast finite-difference solvers for Dirichlet problems on general domains
The author proves the existence of the multi-parameter asymptotic error expansion to the five-point difference scheme for Dirichlet problems for the linear and semilinear elliptic PDE on general domains. By Richardson extrapolation, this expansion leads to a simple process for accelerating the convergence of the method.
Some fast finite-difference solvers for Dirichlet problems on special domains
The author proves the existence of the multi-parameter asymptotic error expansion to the usual five-point difference scheme for Dirichlet problems for the linear and semilinear elliptic PDE on the so-called uniform and nearly uniform domains. This expansion leads, by Richardson extrapolation, to a simple process for accelerating the convergence of the method. A numerical example is given.
Some fast finite-difference solvers for two-dimensional evolutionary equations on special domains
The author proves the existence of the asymptotic error expansion to the Peaceman-Rachford finite-difference scheme for the first boundary value problem of the two-dimensional evolationary equation on the so-called uniform and nearly uniform domains. This expansion leads, by Richardson extrapolation, to a simple process for accelerating the convergence of the method. A numerical example is given.
Some iterative Poisson solvers applied to numerical solution of the model fourth-order elliptic problem
The numerical solution of the model fourth-order elliptic boundary value problem in two dimensions is presented. The iterative procedure in which the biharmonic operator is splitted into two Laplace operators is used. After formulating the finite-difference approximation of the procedure, a formula for the evaluation of the transformed iteration vectors is developed. The Jacobi semi-iterative, Richardson and A.D.I. iterative Poisson solvers are applied to compute one transformed iteration vector....
Some -error estimates for semi-variational method applied to parabolic equations
Some mixed finite element methods on anisotropic meshes
The paper deals with some mixed finite element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived in some anisotropic weighted Sobolev spaces. As particular applications, the numerical approximation by mixed methods of the Laplace equation in domains with edges is investigated where anisotropic finite element meshes are appropriate. Optimal error estimates are obtained using some anisotropic...
Some mixed finite element methods on anisotropic meshes
The paper deals with some mixed finite element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived in some anisotropic weighted Sobolev spaces. As particular applications, the numerical approximation by mixed methods of the Laplace equation in domains with edges is investigated where anisotropic finite element meshes are appropriate. Optimal error estimates are obtained using some anisotropic...
Some modifications of finite-difference schemes for the elliptic singular problem
Some modifications of the classic five point finite-difference scheme for the mixed problem for the Laplace equation
Some new convergence results in finite element theories for elliptic problems
Some new error estimates for finite element methods for second order hyperbolic equations using the Newmark method
We consider a family of conforming finite element schemes with piecewise polynomial space of degree in space for solving the wave equation, as a model for second order hyperbolic equations. The discretization in time is performed using the Newmark method. A new a priori estimate is proved. Thanks to this new a priori estimate, it is proved that the convergence order of the error is in the discrete norms of and , where and are the mesh size of the spatial and temporal discretization, respectively....
Some New Families of Finite Elements for the Stokes Equations.
Some nonstandard finite element estimates with applications to Poisson and Signorini problems.
Some remarks concerning stabilization techniques for convection--diffusion problems
There are many methods and approaches to solving convection--diffusion problems. For those who want to solve such problems the situation is very confusing and it is very difficult to choose the right method. The aim of this short overview is to provide basic guidelines and to mention the common features of different methods. We place particular emphasis on the concept of linear and non-linear stabilization and its implementation within different approaches.
Some remarks on averaging in the BDDC method
In this paper, we introduce a general framework for derivation of the averaging operator, from which the standard choices are recovered by simplifications. Then, an alternative approach derived by another simplification is proposed and tested on a 2D example.
Some results on semilinear systems on the unbounded space R3.
We study in this paper some systems, using standard tools devoted to the analysis of semilinear elliptic problems on R3. These systems do not admit any non trivial radial solutions in the E1 E2 = + 1 cases. A first type of solution consists in a ground state of R (-1,-1), exhibited by variational arguments, whose structure is a finite energy perturbation of a non trivial constant solution of R (-1,-1). A second type consists in a radial, oscillating, asymptotically null at infinity solution in the...
Some superconvergence results of high-degree finite element method for a second order elliptic equation with variable coefficients
In this paper, some superconvergence results of high-degree finite element method are obtained for solving a second order elliptic equation with variable coefficients on the inner locally symmetric mesh with respect to a point x 0 for triangular meshes. By using of the weak estimates and local symmetric technique, we obtain improved discretization errors of O(h p+1 |ln h|2) and O(h p+2 |ln h|2) when p (≥ 3) is odd and p (≥ 4) is even, respectively. Meanwhile, the results show that the combination...