The Contraction Number of a Multigrid Method for Solving the Poisson Equation.
The Effect of Quadrature Errors in the Numerical Solution of Two-Dimensional Boundary Value Problems by Variational Techniques (Short Communication)
The Effect of Quadrature Errors in the Numerical Solution of Two-Dimensional Boundary Value Problems by Variational Techniques
The Frequency Decomposition Multi-Grid Method. Part I: Application to Anisotropic Equations.
The method of fictitious right-hand sides
The paper deals with the application of a fast algorithm for the solution of finite-difference systems for boundary-value problems on a standard domain (e.g. on a rectangle) to the solution of a boundary-value problem on a domain of general shape contained in the standard domain. A simple iterative procedure is suggested for the determination of fictitious right-hand sides for the system on the standard domain so that its solution is the desired one. Under the assumptions that are usual for matrices...
The Neumann-Dirichlet Domain Decomposition Method with Inexact Solvers on the Subdomains.
The Numerical Solution of a Periodic Parabolic Problem Subject to a Nonlinear Boundary Condition. II.
The Ordering of Tridiagonal Matrices in the Cyclic Reduction Method for Poisson's Equation.
The Robbins problem for elliptic equations in space
The strengthened C.B.S. inequality constant for second order elliptic partial differential operator and for hierarchical bilinear finite element functions
We estimate the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for hierarchical bilinear finite element spaces and elliptic partial differential equations with coefficients corresponding to anisotropy (orthotropy). It is shown that there is a nontrivial universal estimate, which does not depend on anisotropy. Moreover, this estimate is sharp and the same as for hierarchical linear finite element spaces.
Three-level Alternating Direction Implicit Iterative methods for Solving the Dirichlet Problem
Transfer of boundary conditions for difference equations
It is well-known that the idea of transferring boundary conditions offers a universal and, in addition, elementary means how to investigate almost all methods for solving boundary value problems for ordinary differential equations. The aim of this paper is to show that the same approach works also for discrete problems, i.e., for difference equations. Moreover, it will be found out that some results of this kind may be obtained also for some particular two-dimensional problems.
Two preconditioners based on the multi-level splitting of finite element spaces.
Two simple derivations of universal bounds for the C.B.S. inequality constant
Universal bounds for the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for piecewise linear-linear and piecewise quadratic-linear finite element spaces in 2 space dimensions are derived. The bounds hold for arbitrary shaped triangles, or equivalently, arbitrary matrix coefficients for both the scalar diffusion problems and the elasticity theory equations.