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

DOI10.1142/s0219876222500487OpenAlexW4296210158MaRDI QIDQ6173071

S. Gowrisankar, Kumar Rajeev Ranjan

Publication date: 21 July 2023

Published in: International Journal of Computational Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219876222500487

zbMATH Keywords

uniform convergencefinite element methodssingular perturbation problemboundary and interior layersthe NIPG methods

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70)

Cites Work

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• Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters
• A coupled continuous-discontinuous FEM approach for convection diffusion equations
• Local projection stabilisation on \(S\)-type meshes for convection-diffusion problems with characteristic layers
• Discontinuous Galerkin least-squares finite element methods for singularly perturbed reaction-diffusion problems with discontinuous coefficients and boundary singularities
• Layer-adapted meshes for convection-diffusion problems
• Singularly perturbed convection--diffusion problems with boundary and weak interior layers.
• Uniform convergence of discontinuous finite element methods for singularly perturbed reaction-diffusion problems
• The streamline-diffusion method for a convection--diffusion problem with a point source
• Study of the NIPG method for two-parameter singular perturbation problems on several layer adapted grids
• Uniformly convergent NIPG method for singularly perturbed convection diffusion problem on Shishkin type meshes
• Continuous-discontinuous finite element method for convection-diffusion problems with characteristic layers
• Higher order uniformly convergent NIPG methods for 1-d singularly perturbed problems of convection-diffusion type
• Parameter uniform optimal order numerical approximation of a class of singularly perturbed system of reaction diffusion problems involving a small perturbation parameter
• Higher order uniformly convergent continuous/discontinuous Galerkin methods for singularly perturbed problems of convection-diffusion type
• Analysis of a new stabilized higher order finite element method for advection-diffusion equations
• Interior penalty discontinuous approximations of convection-diffusion problems with parabolic layers
• A hybrid difference scheme for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient
• The SDFEM for singularly perturbed convection–diffusion problems with discontinuous source term arising in the chemical reactor theory
• Two-Level Defect-Correction Stabilized Finite Element Method for the Incompressible Navier–Stokes Equations Based on Pressure Projection
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• An Interior Penalty Finite Element Method with Discontinuous Elements
• Finite Element Methods for Elliptic Equations Using Nonconforming Elements
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• Analysis of a Galerkin finite element method on a Bakhvalov-Shishkin mesh for a linear convection-diffusion problem
• A second-order scheme for singularly perturbed differential equations with discontinuous source term
• Finite element superconvergence on Shishkin mesh for 2-D convection-diffusion problems
• Method of Order Reduction for the High-Dimensional Convection-Diffusion-Reaction Equation with Robin Boundary Conditions Based on MQ RBF-FD
• The Local Singular Boundary Method for Solution of Two-Dimensional Advection–Diffusion Equation
• Discontinuous Legendre Wavelet Element Method for Reaction–Diffusion Equation from Mathematical Chemistry
• A Method for the Numerical Solution of a Boundary Value Problem for a Linear Differential Equation with Interval Parameters
• A supercloseness result for the discontinuous Galerkin stabilization of convection–diffusion problems on Shishkin meshes

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