Results 171 to 180 of about 1,916 (200)

NIPG Method on Shishkin Mesh for Singularly Perturbed Convection–Diffusion Problem with Discontinuous Source Term

International Journal of Computational Methods, 2022
In this paper, we provide numerical approaches for singularly perturbed convection–diffusion problem with a discontinuous source term. As a result of the discontinuity in the source term, the problem highlights an exponential-type boundary layer and a weak interior layer.
Kumar Rajeev Ranjan, S. Gowrisankar
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Finite difference numerical solution of Troesch’s problem on a piecewise uniform Shishkin mesh

Calcolo, 2016
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Temimi, Helmi, Ben-Romdhane, Mohamed, Ansari, Ali R., Shishkin, Grigorii I.   +3 more
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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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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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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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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
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Clavero, C., Gracia, J. L., Lisbona, F.
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On biorthogonal approximation of solutions of some boundary value problems on Shishkin mesh

AIP Conference Proceedings, 2020
Singularly perturbed boundary value problems are widely studied in applied problems of physics and engineering. However, their solutions are rarely possible to construct in an explicit form, so numerical methods of solving such problems are actively studied.
E. Kulikov, A. Makarov
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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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