ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991):65J10, 65M12, 65M15, 35B32, 58F14
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. We consider semidiscretizations in time, based on the backward Euler method, of an abstract, non-autonomous parabolic initial value problem \[ u'(t) = A(t)u(t); \quad u(0) = u_0, \] where $A(t) : D(A(t)) \subset X \to X$ , $0 \le t \le T$ , is a family of sectorial operators in a Banach space X. The domains $D(A(t))$ are allowed to depend on t. Our hypotheses are fulfilled for classical parabolic problems in the $L^p$ , $1 〈 p 〈+\infty$ , norms. We prove that the semidiscretization is stable in a suitable sense. We get optimal estimates for the error even when non-homogeneous boundary values are considered. In particular, the results are applicable to the analysis of the semidiscretizations of time-dependent parabolic problems under non-homogeneous Neumann boundary conditions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050427
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