NIPG Finite Element Method for Convection-Dominated Diffusion Problems with Discontinuous Data

DOI10.1142/s0219876223500019OpenAlexW4315782176MaRDI QIDQ6173095

Kapil K. Sharma, Ram Prasad Yadav, Pratima Rai

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/s0219876223500019

zbMATH Keywords

convection-diffusion problemssingularly perturbed problemdiscontinuous databoundary layerShishkin meshinterior layerdiscontinuous Galerkin finite element method

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Cites Work

• Unnamed Item
• Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary-value problems
• Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems
• A brief survey on numerical methods for solving singularly perturbed problems
• Discontinuous Galerkin least-squares finite element methods for singularly perturbed reaction-diffusion problems with discontinuous coefficients and boundary singularities
• Asymptotic and numerical analysis of singular perturbation problems: A survey
• Numerical solution of the three-dimensional advection--diffusion equation.
• A parameter-uniform Schwarz method for a singularly perturbed reaction-diffusion problem with an interior layer
• The streamline-diffusion method for a convection--diffusion problem with a point source
• Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I
• Convergence analysis of weak Galerkin flux-based mixed finite element method for solving singularly perturbed convection-diffusion-reaction problem
• Higher order accurate approximations on equidistributed meshes for boundary layer originated mixed type reaction diffusion systems with multiple scale nature
• A moving mesh refinement based optimal accurate uniformly convergent computational method for a parabolic system of boundary layer originated reaction-diffusion problems with arbitrary small diffusion terms
• Finite element method on Shishkin mesh for a singularly perturbed problem with an interior layer
• Higher order uniformly convergent NIPG methods for 1-d singularly perturbed problems of convection-diffusion type
• On discontinuous Galerkin finite element method for singularly perturbed delay differential equations
• A numerical method for solving boundary and interior layers dominated parabolic problems with discontinuous convection coefficient and source terms
• An a posteriori based convergence analysis for a nonlinear singularly perturbed system of delay differential equations on an adaptive mesh
• Parameter uniform optimal order numerical approximation of a class of singularly perturbed system of reaction diffusion problems involving a small perturbation parameter
• Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convec\-tion coefficient
• Interior penalty discontinuous approximations of convection-diffusion problems with parabolic layers
• On the numerical solution of the one-dimensional convection-diffusion equation
• The SDFEM for singularly perturbed convection–diffusion problems with discontinuous source term arising in the chemical reactor theory
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• Difference Methods for Singular Perturbation Problems
• Numerical treatment of two‐parameter singularly perturbed parabolic convection diffusion problems with non‐smooth data
• A second-order scheme for singularly perturbed differential equations with discontinuous source term
• A graded mesh refinement approach for boundary layer originated singularly perturbed time‐delayed parabolic convection diffusion problems
• A higher order difference method for singularly perturbed parabolic partial differential equations
• Sufficient conditions for uniform convergence on layer-adapted grids

This page was built for publication: NIPG Finite Element Method for Convection-Dominated Diffusion Problems with Discontinuous Data