Layton, W.; Polman, B. Oscillation absorption finite element methods for convection-diffusion problems. (English) Zbl 0860.65112 SIAM J. Sci. Comput. 17, No. 6, 1328-1346 (1996). The authors propose a new method of eliminating overshoots and undershoots when using finite element methods for convection dominated convection-diffusion problems by including a penalty term based on a priori bounds for the solution determined by a maximum principle. The resulting nonlinear system is solved by Newton iteration which may be costly. Numerical examples are given. Reviewer: J.D.P.Donnelly (Oxford) Cited in 3 Documents MSC: 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65H10 Numerical computation of solutions to systems of equations 35J65 Nonlinear boundary value problems for linear elliptic equations 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs Keywords:oscillation absorption; nonlinear absorption; monotone operators; overshoot-undershoot elimination; numerical examples; finite element methods; convection-diffusion problems; penalty term; maximum principle; Newton iteration PDFBibTeX XMLCite \textit{W. Layton} and \textit{B. Polman}, SIAM J. Sci. Comput. 17, No. 6, 1328--1346 (1996; Zbl 0860.65112) Full Text: DOI