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Oscillation absorption finite element methods for convection-diffusion problems. (English) Zbl 0860.65112

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.

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
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