Results 151 to 160 of about 225 (176)

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.
Xiaowei Liu 0002, Jin Zhang 0004
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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.
P. Maragatha Meenakshi, S. Valarmathi, John J. H. Miller   +2 more
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Supercloseness in a balanced norm of the NIPG method on Shishkin mesh for a reaction diffusion problem

Applied Mathematics and Computation, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaoqi Ma, Jin Zhang 0004
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A Priori Estimates for the Solution of Convection-Diffusion Problems and Interpolation on Shishkin Meshes

Zeitschrift für Analysis und ihre Anwendungen, 1997
The solution of singularly perturbed convection-diffusion problems can be split into a regular and a singular part containing the boundary layer terms. In dimensions n = 1 and n = 2
Dobrowolski, M., Roos, H.-G.
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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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The ε‐Uniform Convergence of a Defect‐Correction Method on a Shishkin Mesh

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2001
AbstractA 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 accuracy of the central difference scheme.
A. Fróhner, T. Linss, H.‐G. Roos
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A supercloseness result for the discontinuous Galerkin stabilization of convection–diffusion problems on Shishkin meshes

Numerical Methods for Partial Differential Equations, 2007
AbstractWe consider a convection–diffusion problem with Dirichlet boundary conditions posed on a unit square. The problem is discretized using a combination of the standard Galerkin FEM and an h–version of the nonsymmetric discontinuous Galerkin FEM with interior penalties on a layer–adapted mesh with linear/bilinear elements.
Roos, Hans-Görg, Zarin, Helena
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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
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaowei Liu 0002, Jin Zhang 0004
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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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Carmelo Clavero, Jose L. Gracia, Francisco Javier Lisbona   +2 more
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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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