Results 211 to 220 of about 421,152 (262)

Uniform Pointwise Convergence on Shishkin-Type Meshes for Quasi-Linear Convection-Diffusion Problems

SIAM Journal on Numerical Analysis, 2000
This paper deals with the singularly perturbed quasilinear convection-diffusion problem \[ -\varepsilon u''- b(x,u)u'+ c(x,i)= 0\quad\text{for }x\in (0,1),\quad u(0)= u(1)= 0, \] where \(\varepsilon\ll 1\) is a small positive constant. The authors introduce the finite-difference scheme and discuss its stability and consistency on an arbitrary nonequi ...
Linß, Torsten, Roos, Hans-Görg, Vulanovic, Relja   +2 more
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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
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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
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Stability and convergence analysis on Shishkin mesh for a nonlinear singularly perturbed problem with three-point boundary condition

Quaestiones Mathematicae. Journal of the South African Mathematical Society, 2020
The present study is conducted on finite difference method in Shishkin piecewise uniform mesh in a singularly perturbed boundary value problem for a nonlinear differential equation.
D. Arslan
semanticscholar   +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.
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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
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Uniform superconvergence of a Galerkin finite element method on Shishkin‐type meshes

Numerical Methods for Partial Differential Equations, 2000
This paper deals with a Galerkin finite element method with piecewise bilinear trial and test functions on Shishkin-type meshes for a model singularly perturbed convection-diffusion problem on the unit square. The author studies the convergence of the method with respect to the \(\varepsilon\)-weighted energy norm. From this result, he derives \(L_2\)-
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High order methods on Shishkin meshes for singular perturbation problems of convection–diffusion type

Numerical Algorithms, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Clavero, C., Gracia, J. L., Lisbona, F.
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Pointwise estimates of SDFEM on Shishkin triangular meshes for problems with characteristic layers

Numerical Algorithms, 2017
A Shishkin mesh is a piecewise uniform mesh (or a tensor-product version in more than one dimension). What distinguishes a Shishkin mesh from any other piecewise uniform mesh is the choice of the so-called transition parameter(s), which are the point(s) at wich the mesh size changes abruptly. A different approach is to use layer-adapted meshes.
Liu, Xiaowei, Zhang, Jin
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Pointwise convergence of approximations to a convection–diffusion equation on a Shishkin mesh

Applied Numerical Mathematics, 2000
This paper deals with a singularly perturbed one-dimensional boundary value problem. A standard, centered difference or finite element method on a piecewise equidistant mesh is considered. The author transforms the obtained equations so that the new equations have a monotonicity property and proves pointwise convergence, uniform in the perturbation ...
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