Convergence of the variable two - step BDF time discretisation of nonlinear evolution problems governed by a monotone potential operator
نویسنده
چکیده
The initial-value problem for a first-order evolution equation is discretised in time by means of the two-step backward differentiation formula (BDF) on a variable time grid. The evolution equation is governed by a monotone and coercive potential operator. On a suitable sequence of time grids, the piecewise constant interpolation and a piecewise linear prolongation of the time discrete solution are shown to converge towards the weak solution if the ratios of adjacent step sizes are close to 1 and do not vary too much. AMS subject classification (2000): 65M12, 47J35, 35K55, 47H05, 47H50.
منابع مشابه
Two-step Bdf Time Discretisation of Nonlinear Evolution Problems Governed by Monotone Operators with Stringly Continuous Peryurbations
The time discretisation of the initial-value problem for a first-order evolution equation by the two-step backward differentiation formula (BDF) on a uniform grid is analysed. The evolution equation is governed by a time-dependent monotone operator that might be perturbed by a time-dependent strongly continuous operator. Well-posedness of the numerical scheme, a priori estimates, convergence of...
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