An optimal rational basis function in the finite element method for convection-diffusion problems in one space variables

DOI10.1016/0895-7177(94)90089-2zbMath0802.65097OpenAlexW2087880864MaRDI QIDQ1328850

F. D. Van Niekerk, Anton van Niekerk

Publication date: 7 August 1994

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0895-7177(94)90089-2

zbMATH Keywords

numerical examplesconvection-diffusion problemsupwindingGalerkin finite element methodsrational basis functions

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05)

Cites Work

• A Hermite rational approximation method for the Korteweg-de Vries equation
• A rational basis for second-kind Abel integral equations
• An explicit finite element method for convection-diffusion equations using rational basis functions
• A Galerkin method with rational basis functions for Burgers equation
• Approximate symmetrization and Petrov-Galerkin methods for diffusion- convection problems
• An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable
• A Galerkin method using rational basis functions
• Generation of Finite Difference Formulas on Arbitrarily Spaced Grids
• A fixed grid finite element technique for modelling phase change in steady-state conduction-advection problems
• Finite element methods for second order differential equations with significant first derivatives
• Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations