Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations
نویسندگان
چکیده
منابع مشابه
Maximum-norm Resolvent Estimates for Elliptic Finite Element Operators on Nonquasiuniform Triangulations
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 assum...
متن کاملMaximum-norm estimates for resolvents of elliptic finite element operators
Let Ω be a convex domain with smooth boundary in Rd. It has been shown recently that the semigroup generated by the discrete Laplacian for quasi-uniform families of piecewise linear finite element spaces on Ω is analytic with respect to the maximum-norm, uniformly in the mesh-width. This implies a resolvent estimate of standard form in the maximum-norm outside some sector in the right halfplane...
متن کاملResolvent Estimates for Elliptic Finite Element Operators in One Dimension
We prove the analyticity (uniform in h ) of the semigroups generated on Lp(0, 1), 1 < p < oo , by finite element analogues Ah of a onedimensional second-order elliptic operator A under Dirichlet boundary conditions. This is accomplished by showing the appropriate estimates for the resolvents by means of energy arguments. The results are applied to prove stability and optimal-order error bounds ...
متن کاملMaximum-norm Stability, Smoothing and Resolvent Estimates for Parabolic Finite Element Equations
We survey work on stability and smoothing estimates in maximum-norm for spatially semidiscrete finite element approximations of a model parabolic equation, and related such estimates for the resolvent of the corresponding discrete elliptic operator. We end with a short discussion of stability of fully discrete time stepping methods. Résumé. Nous présentons un bilan des résultats sur la stabilit...
متن کاملResolvent estimates of elliptic differential and finite-element operators in pairs of function spaces
We present some resolvent estimates of elliptic differential and finite-element operators in pairs of function spaces, for which the first space in a pair is endowed with stronger norm. In this work we deal with estimates in (Lebesgue, Lebesgue), (Hölder, Lebesgue), and (Hölder, Hölder) pairs of norms. In particular, our results are useful for the stability and error analysis of semidiscrete an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ESAIM: Mathematical Modelling and Numerical Analysis
سال: 2006
ISSN: 0764-583X,1290-3841
DOI: 10.1051/m2an:2006040