Smoothing properties and approximation of time derivatives for parabolic equations: variable time steps
Artikel i vetenskaplig tidskrift, 2003

Abstract We study smoothing properties and approximation of time derivatives for time discretization schemes with variable time steps for a homogeneous parabolic problem formulated as an abstract initial value problem in a Banach space. The time stepping methods are based on using rational approximations to the exponential function which are A()-stable for suitable (0,/2] with unit bounded maximum norm. First- and second-order approximations of time derivatives based on using difference quotients are considered. Smoothing properties are derived and error estimates are established under the so-called increasing quasi-quasiuniform assumption on the time steps.


Yubin Yan

Göteborgs universitet

Chalmers, Institutionen för beräkningsmatematik

BIT (Copenhagen)

0006-3835 (ISSN) 15729125 (eISSN)

Vol. 43 3 647-669



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