Results 71 to 80 of about 421,152 (262)

Pointwise convergence of the local discontinuous Galerkin method on a Shishkin mesh for 2D reaction-diffusion problems

ESAIM: Mathematical Modelling and Numerical Analysis
A local discontinuous Galerkin (LDG) method, based on  a recently-developed ``layer-upwind" flux, is applied on a Shishkin mesh to solve a reaction-diffusion problem posed on the 2D unit square.
Yao Cheng, Xuesong Wang, Martin Stynes
openalex   +2 more sources

Preconditioning and Uniform Convergence for Convection-Diffusion Problems Discretized on Shishkin-Type Meshes [PDF]

Advances in Numerical Analysis, 2016
A one-dimensional linear convection-diffusion problem with a perturbation parameter ɛ multiplying the highest derivative is considered. The problem is solved numerically by using the standard upwind scheme on special layer-adapted meshes. It is proved that the numerical solution is ɛ-uniform accurate in the maximum norm.
Nhan, Thái Ahn, Vulanović, Relja
openaire   +1 more source

Comparison of adaptive meshes for a singularly perturbed reaction–diffusion problem

Mathematical Modelling and Analysis, 2012
We consider a singular second-order boundary value problem. The differential problem is approximated by the Galerkin finite element scheme. The main goal is to compare the well known apriori Bakhvalov and Shishkin meshes with the adaptive mesh based on ...
Andrej Bugajev, Raimondas Čiegis
doaj   +1 more source

A Layer-Adapted Numerical Method for Singularly Perturbed Partial Functional-Differential Equations

Axioms
This article describes an effective computing method for singularly perturbed parabolic problems with small negative shifts in convection and reaction terms. To handle the small negative shifts, the Taylor series expansion is used.
Ahmed A. Al Ghafli, Fasika Wondimu Gelu, Hassan J. Al Salman   +2 more
doaj   +1 more source

Stabilization arising from PGEM : a review and further developments [PDF]

, 2009
The aim of this paper is twofold. First, we review the recent Petrov-Galerkin enriched method (PGEM) to stabilize numerical solutions of BVP's in primal and mixed forms.
Araya, Araya, Araya, Arnold, Baiocchi, Bank, Barrenechea, Barrenechea, Barrenechea, Brezzi, Brezzi, Brezzi, Brezzi, Brezzi, Brezzi, Brooks, Cangiani, Clément, Ern, Franca, Franca, Franca, Franca, Franca, Franca, Franca, Frédéric Valentin, Gabriel R. Barrenechea, Girault, Hughes, Hughes, Leopoldo P. Franca, Linb, Pierre, Rodolfo Araya, Roos, Stynes, Thomée   +37 more
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Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations

Journal of Mathematics, 2021
In this paper, we consider a class of singularly perturbed advanced-delay differential equations of convection-diffusion type. We use finite and hybrid difference schemes to solve the problem on piecewise Shishkin mesh.
P. Hammachukiattikul, E. Sekar, A. Tamilselvan, R. Vadivel, N. Gunasekaran, Praveen Agarwal   +5 more
doaj   +1 more source

Cholesky factorisation of linear systems coming from finite difference approximations of singularly perturbed problems

, 2015
We consider the solution of large linear systems of equations that arise when two-dimensional singularly perturbed reaction-diffusion equations are discretized.
Madden, Niall, Nhan, Thái Anh
core   +1 more source

Computing Optical Properties of Ultra-thin Crystals [PDF]

, 2016
An overview is given of recent advances in experimental and theoretical understanding of optical properties of ultra-thin crystal structures (graphene, phosphorene, silicene, MoS2, MoSe2 , WS2 , WSe2 , h-AlN, h-BN, fluorographene, graphane).
Albrecht, Attaccalite, Barawi, Bechstedt, Bernardi, Cakir, Cakir, Cao, Ceperley, Chae, Cheiwchanchamnangij, Chen, Cheng, Cheng, Chernikov, Chien, Cudazzo, Debbichi, Despoja, Eda, Fang, Fano, Feng, Feng, Fuchs, Furchi, Gao, Geim, Giannozzi, Gokus, Gong, Gonze, Gourmelon, Gunasinghe, Gutiérrez, Havener, He, He, Heyd, Huang, Huo, Island, Jin, Jing, Jones, Joswig, Kadi, Kang, Karlický, Karlický, Komsa, Kresse, Kresse, Kresse, Kresse, Latini, Lee, Li, Lin, Luo, Mai, Mak, Mak, Mak, Mak, Mak, Marini, Matthes, Mitioglu, Mohan, Nair, Novoselov, Onida, Palummo, Pan, Perdew, Perdew, Pereira, Phillips, Prezzi, Pulci, Qiu, Ramasubramaniam, Rayson, Rivera, Rohlfing, Ross, Samarakoon, Sanchez, Sedelnikova, Seixas, Shang, Shi, Shih, Shishkin, Shishkin, Shishkin, Singh, Splendiani, Srivastava, Sun, Tongay, Tongay, Tongay, Tonndorf, Tran, Trevisanutto, Ugeda, Wachsmuth, Wang, Wang, Wang, Wei, Wei, Wie, Withers, Xia, Yamamoto, Yan, Yan, Yang, Yang, Yang, Yang, Yang, Ye, You, Yuan, Zeng, Zhou   +129 more
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A parameter uniform numerical method for singularly perturbed delay problems with discontinuous convection coefficient

Arab Journal of Mathematical Sciences, 2016
In this paper a standard numerical method with piecewise linear interpolation on Shishkin mesh is suggested to solve singularly perturbed boundary value problem for second order ordinary delay differential equations with discontinuous convection ...
V. Subburayan
doaj   +1 more source

Construction of a global solution for the one dimensional singularly-perturbed boundary value problem

, 2017
We consider an approximate solution for the one-dimensional semilinear singularly-perturbed boundary value problem, using the previously obtained numerical values of the boundary value problem in the mesh points and the representation of the exact ...
Barakovic, Elvis, Duvnjaković, Enes, Karasuljić, Samir, Pasic, Vedad   +3 more
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