Solving neutron transport problems with sharp layers on the Shishkin mesh
Progress in Nuclear EnergyTseelmaa Byambaakhuu, Dean Wang
semanticscholar +3 more sources
Advantages of the Samarskii-type schemes on the Shishkin mesh
Journal of Computational and Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Relja Vulanović, Thái Anh Nhan
openaire +3 more sources
Partial Differential Equations in Applied Mathematics, 2023 This work presents a numerical solution to singularly perturbed Robin-type parabolic convection–diffusion problems. A hybrid method that combines the central difference scheme in the inner region and the midpoint of the upwind scheme in the outer region ...
Fasika Wondimu Gelu +1 more
doaj +2 more sources
On biorthogonal approximation of solutions of some boundary value problems on Shishkin mesh [PDF]
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. K. Kulikov, А. А. Макаров
openalex +2 more sources
Convergence analysis of a weak Galerkin finite element method on a Shishkin mesh for a singularly perturbed fourth-order problem in 2D [PDF]
Journal of Computational and Applied Mathematics, 2023 We consider the singularly perturbed fourth-order boundary value problem $\varepsilon ^{2}\Delta ^{2}u-\Delta u=f $ on the unit square $\Omega \subset \mathbb{R}^2$, with boundary conditions $u = \partial u / \partial n = 0$ on $\partial \Omega$, where $\
Shicheng Liu, Xiangyun Meng, Qilong Zhai
openalex +3 more sources
Supercloseness of the NIPG method for a singularly perturbed convection diffusion problem on Shishkin mesh in 2D [PDF]
Computers and Mathematics with Applications, 2023 As a popular stabilization technique, the nonsymmetric interior penalty Galerkin (NIPG) method has significant application value in computational fluid dynamics.
Xiaoqi Ma, Jin Zhang
openalex +3 more sources
An Upwind Finite Difference Method to Singularly Perturbed Convection Diffusion Problems on a Shishkin Mesh [PDF]
arXiv.org, 2023 This paper introduces a numerical approach to solve singularly perturbed convection diffusion boundary value problems for second-order ordinary differential equations that feature a small positive parameter {\epsilon} multiplying the highest derivative ...
Daniel T. Gregory
openalex +3 more sources
Uniform convergence of optimal order under a balanced norm of a local discontinuous Galerkin method on a Shishkin mesh [PDF]
arXiv.org, 2022 For singularly perturbed reaction-diffusion problems in 1D and 2D, we study a local discontinuous Galerkin (LDG) method on a Shishkin mesh. In these cases, the standard energy norm is too weak to capture adequately the behavior of the boundary layers that
Jin Zhang, Wenchao Zheng
openalex +3 more sources
Supercloseness of the SDFEM on Shishkin triangular meshes for problems with exponential layers [PDF]
Advances in Computational Mathematics, 2016 In this paper, we analyze the supercloseness property of the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes, which is different from one in the case of rectangular meshes. The analysis depends on integral inequalities for the part related to the diffusion in the bilinear form.
Jin Zhang, Xiaowei Liu
openalex +5 more sources
Supercloseness of the DDG method for a singularly perturbed convection diffusion problem on Shishkin mesh [PDF]
arXiv.orgThis paper investigates the supercloseness of a singularly perturbed convection diffusion problem using the direct discontinuous Galerkin (DDG) method on a Shishkin mesh.
Xiaoqi Ma +3 more
semanticscholar +3 more sources