Author(s) :
Etienne Emmrich
The paper is published :
J. Appl. Math. & Computing
MSC 2000
- 65M12 Stability and convergence of numerical methods
-
65J15 Equations with nonlinear operators
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35K90 Abstract parabolic evolution equations
-
47J35 Nonlinear evolution equations
Abstract :
The temporal discretisation of a moderate semilinear parabolic problem in an abstract setting by the two-step backward
differentiation formula with variable step sizes is analysed.
Stability as well as optimal smooth data error estimates are derived if the ratios of
adjacent step sizes are bounded from above by 1.91.
Keywords :
semilinear parabolic problem; time discretization; backward differentiation formula; non-uniform grid; stability; error estimate