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Super-convergence of the a posteriori error estimators for finite-element solutions

C̆iegis R.

Demonstratio Mathematica

2003

Vol. 36, nr 2

495--506

The finite difference scheme for the solution of one quasilinear equation

Ciegis R., Ciegis R., Rate P.

Demonstratio Mathematica

2001

Vol. 34, nr 3

723-732

In this paper we are interested in the solution of one-dimensional quasi-linear diffusion-reaction equation. The nonlinear reaction term includes the first derivative in space of the solution. We use the finite difference method to discretize this problem. The modification of a general methodology for investigation of difference schemes approximating non-stationary differential equations is used and the results for the stability and convergence of the numerical solution are proved. The convergence of the discrete derivative of the solution is proved in the maximum norm.