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- Crouzeix, Michel, et al.
(författare)
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The stability of rational approximations of analytic semigroups
- 1993
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Ingår i: BIT Numer. Math.. - 0006-3835 .- 1572-9125. ; 33:1, s. 74-84
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Tidskriftsartikel (refereegranskat)abstract
- This paper contains two new characterizations of generators of analytic semigroups of linear operators in a Banach space. These characterizations do not require use of complex numbers. One is used to give a new proof that strongly elliptic second order partial differential operators generate analytic semigroups inL p , 1
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- Thomee, Vidar, 1933, et al.
(författare)
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Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations
- 2006
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Ingår i: M2AN Math. Model. Numer. Anal.. - : EDP Sciences. - 0764-583X .- 2822-7840 .- 1290-3841. ; 40:5, s. 923-937
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Tidskriftsartikel (refereegranskat)abstract
- In recent years several papers have been devoted to stability and smoothing properties in maximum-norm of finite element discretizations of parabolic problems. Using the theory of analytic semigroups it has been possible to rephrase such properties as bounds for the resolvent of the associated discrete elliptic operator. In all these cases the triangulations of the spatial domain has been assumed to be quasiuniform. In the present paper we show a resolvent estimate, in one and two space dimensions, under weaker conditions on the triangulations than quasiuniformity. In the two-dimensional case, the bound for the resolvent contains a logarithmic factor.
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