A note of pointwise estimates on Shishkin meshes [PDF]
, 2012 We propose the estimates of the discrete Green function for the stream- line diffusion finite element method (SDFEM) on Shishkin meshes.Comment: 10pages, 1 ...
Zhang, Jin
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Numerical Scheme for Singularly Perturbed Mixed Delay Differential Equation on Shishkin Type Meshes [PDF]
Fractal and Fractional, 2022 Two non-uniform meshes used as part of the finite difference method to resolve singularly perturbed mixed-delay differential equations are studied in this article.
Sekar Elango, Bundit Unyong
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A parameter uniform method for two-parameter singularly perturbed boundary value problems with discontinuous data [PDF]
MethodsX, 2023 We consider two-parameter singularly perturbed problems of reaction-convection-diffusion type in one dimension. The convection coefficient and source term are discontinuous at a point in the domain.
Nirmali Roy, Anuradha Jha
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Layer resolving numerical scheme for singularly perturbed parabolic convection-diffusion problem with an interior layer [PDF]
MethodsX, 2023 Singularly perturbed parabolic convection-diffusion problem with interior layer is a type of singularly perturbed boundary value problems which have sign change properties in the coefficient function of the convection term.
Gemadi Roba Kusi +2 more
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A numerical algorithm to computationally solve the Hemker problem using Shishkin meshes [PDF]
Journal of Computational and Applied Mathematics, 2020 25 pages with 8 ...
Alan F. Hegarty, Eugene O’Riordan
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Finite element superconvergence on Shishkin mesh for 2-D convection-diffusion problems [PDF]
Mathematics of Computation, 2003 This paper deals with the standard finite element method combined with a Shishkin mesh strategy for a convection-diffusion problem \[ -\varepsilon\Delta u+ \vec\beta\nabla u+ cu= f\text{ in }\Omega= (0,1)\times (0, 1),\;u= 0\text{ on }\partial\Omega, \] where \(\varepsilon\) is a small positive number.
Zhimin Zhang
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Local Projection Stabilization Method of Convective-Diffusion Problem on Shishkin Triangular Mesh [PDF]
, 2023 In this paper, a singularly perturbed convection-diffusion problem with exponential boundary layers is considered. For this problems, we study a local projection stabilization method on a Shishkin triangular mesh. If piecewise polynomials of order r ≥ 1 are used, the method has uniform convergence of almost order r in the energy norm.
Shasha Liu, Xiaowei Liu
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Analysis of SDFEM on Shishkin Triangular Meshes and Hybrid Meshes for Problems with Characteristic Layers [PDF]
Journal of Scientific Computing, 2016 In this paper, we analyze the streamline diffusion finite element method (SDFEM) for a model singularly perturbed convection-diffusion equation on a Shishkin triangular mesh and hybrid meshes. Supercloseness property of $u^I-u^N$ is obtained, where $u^I$ is the interpolant of the solution $u$ and $u^N$ is the SDFEM's solution.
Jin Zhang, Xiaowei Liu
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Discrete Green functions of the SDFEM on Shishkin triangular meshes [PDF]
, 2015 9 pages, 2 ...
Zhang Jin
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Shishkin mesh simulation: A new stabilization technique for convection–diffusion problems [PDF]
Computer Methods in Applied Mechanics and Engineering, 2012 Abstract A new stabilization procedure is presented. It is based on a simulation of the interaction between the coarse and fine parts of a Shishkin mesh, but can be applied on coarse and irregular meshes and on domains with nontrivial geometries. The technique, which does not require adjusting any parameter, can be applied to different stabilized and
Bosco Garcı́a-Archilla
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