Results 161 to 170 of about 1,916 (200)

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   +4 more sources

A modification of the Shishkin discretization mesh for one-dimensional reaction–diffusion problems

Applied Mathematics and Computation, 2013
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Vulanović, Relja, Teofanov, Ljiljana
openaire   +3 more sources

A hybrid difference scheme on a Shishkin mesh for linear convection–diffusion problems

Applied Numerical Mathematics, 1999
A difference scheme on a special piecewise equidistant tensor-product mesh (a Shishkin mesh) is considered for a model singularly perturbed convection-diffusion problem in two dimensions. The hybrid method chooses between upwinding and central differencing, depending on the local mesh width in each coordinate direction. It is proved that this method is
Linß, Torsten, Stynes, Martin
openaire   +3 more sources

Galerkin finite element methods for convection–diffusion problems with exponential layers on Shishkin triangular meshes and hybrid meshes

Applied Mathematics and Computation, 2017
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Liu, Xiaowei, Zhang, Jin
openaire   +3 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

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
Fröhner, Anja, Linß, Torsten, Roos, Hans-Görg   +2 more
openaire   +2 more sources

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.
Linß, Torsten, Stynes, Martin
openaire   +2 more sources

Numerical methods on Shishkin meshes for linear convection–diffusion problems

Computer Methods in Applied Mechanics and Engineering, 2001
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Linß, Torsten, Stynes, Martin
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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

Solving a partially singularly perturbed initial value problem on Shishkin meshes

Applied Mathematics and Computation, 2010
The authors analyse a new numerical method for the solution of partially singularly perturbed systems of two coupled ordinary differential equations. Partially singularly perturbed is understood in the sense that one of the coupled equations is singularly perturbed while the other is not.
Meenakshi, P. Maragatha, Valarmathi, S., Miller, J. J. H.   +2 more
openaire   +1 more source