Results 141 to 150 of about 225 (176)

Finite difference numerical solution of Troesch’s problem on a piecewise uniform Shishkin mesh

Calcolo, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ali R Ansari, Mohamed Ben-Romdhane, Grigorii Shishkin   +2 more
exaly   +3 more sources

Defect correction on Shishkin-type meshes

Numerical Algorithms, 2001
The authors consider a defect-correction method that combines a first-order upwinded difference scheme with a second-order central difference scheme for a model singularly perturbed convection-diffusion problem in one dimension on a class of Shishkin-type meshes. They give the first general proof of uniform second-order convergence of this method. As a
Anja Fröhner, Torsten Linß, Hans-Görg Roos   +2 more
openaire   +2 more sources

Supercloseness in a balanced norm of finite element methods on Shishkin and Bakhvalov–Shishkin rectangular meshes for reaction–diffusion problems

Mathematical Methods in the Applied Sciences, 2021
We present a convergence analysis for finite element methods of any order, which are applied on Shishkin mesh and Bakhvalov–Shishkin mesh to a singularly perturbed reaction–diffusion problem. A new interpolant is introduced for analysis in the balanced norm.
Jin Zhang, Xiaowei Liu
openaire   +1 more source

The sdfem on Shishkin meshes for linear convection-diffusion problems

Numerische Mathematik, 2001
The authors consider a modified streamline diffusion finite element method (SDFEM) in order to resolve the boundary layer in some 2D singularly perturbed linear elliptic problems. They use piecewise linear functions on highly nonuniform Shishkin meshes.
Torsten Linß, Martin Stynes
openaire   +2 more sources

Numerical methods on Shishkin meshes for linear convection–diffusion problems

Computer Methods in Applied Mechanics and Engineering, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Linß, Torsten, Stynes, Martin
openaire   +2 more sources

A finite difference analysis of a streamline diffusion method on a Shishkin mesh

Numerical Algorithms, 1998
The authors consider a singularly perturbed convection-diffusion boundary value problem whose solution has a single boundary layer. They use the streamline diffusion finite element method (SDFEM) to solve the problem. In fact, this SDFEM generates a finite differences scheme which satisfies a discrete maximum principle.
Martin Stynes, Lutz Tobiska
openaire   +1 more source

Richardson extrapolation for a convection–diffusion problem using a Shishkin mesh

Applied Numerical Mathematics, 2003
For the solution of a linear two-point convection-diffusion boundary value problem the authors consider a simple upwind scheme on a piecewise uniform Shishkin type mesh. An application of Richardson's extrapolation principle improves the convergence rate in the discrete \(L_\infty\) norm from \(O(N^{-1} \ln N)\) to \(O(N^{-2} \ln^2 N)\).
Natividad, Maria Caridad, Stynes, Martin
openaire   +2 more sources

Pointwise error estimates of the bilinear SDFEM on Shishkin meshes

Numerical Methods for Partial Differential Equations, 2012
AbstractA model singularly perturbed convection–diffusion problem in two space dimensions is considered. The problem is solved by a streamline diffusion finite element method (SDFEM) that uses piecewise bilinear finite elements on a Shishkin mesh. We prove that the method is convergent, independently of the diffusion parameter ε, with a pointwise ...
Zhang, Jin, Mei, Liquan
openaire   +2 more sources

The -uniform convergence of a defect correction method on a Shishkin mesh

Applied Numerical Mathematics, 2001
A defect correction method based on finite difference schemes is considered for a singularly perturbed boundary value problem on a Shishkin mesh. The method combines the stability of the upwind difference scheme and the higher-order convergence of the central difference scheme.
Anja Fröhner, Hans-Görg Roos
openaire   +1 more source

A note on the conditioning of upwind schemes on Shishkin meshes

IMA Journal of Numerical Analysis, 1996
The discretization of the singularly perturbed convection-diffusion boundary value problems is presented. For this discretization upwind schemes on a Shishkin mesh are used. The conditioning of these upwind finite difference schemes (UFDS) is investigated.
openaire   +2 more sources