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Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations

Nikolai Yu. Bakaev, Michel Crouzeix, Vidar Thomée (2006)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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,...

Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations

Nikolai Yu. Bakaev, Michel Crouzeix, Vidar Thomée (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

Maximum-Norm Stability and Error Estimates in Galerkin Methods for Parabolic Equations in One Space Variable

V. Thomée, L.B. Wahlbin (1983)

Numerische Mathematik

Mean curvature and the heat equation.

M. van den Berg, J.F. Le Gall (1994)

Mathematische Zeitschrift

Mean transit time and mean residence time for linear diffusion-convection-reaction transport system.

Waniewski, Jacek (2007)

Computational & Mathematical Methods in Medicine

Mean value and Harnack inequalities for a certain class of degenerate parabolic equations.

José C. Fernandes (1991)

Revista Matemática Iberoamericana

In this paper we study the behavior of degenerate parabolic equations of the formv(x) ut(x,t) = Σni,j=1 Dxi (aij(x,t) Dxi u(x,t)),where the coefficients are measurable functions.

Mean value and Harnack inequalities for degenerate parabolic equations

Cristian E. Gutiérrez, Richard L. Wheeden (1990)

Colloquium Mathematicae

Mean value densities for temperatures

N. Suzuki, N. A. Watson (2003)

Colloquium Mathematicae

A positive measurable function K on a domain D in $ℝ^{n + 1}$ is called a mean value density for temperatures if $u (0, 0) = \int \int_{D} K (x, t) u (x, t) d x d t$ for all temperatures u on D̅. We construct such a density for some domains. The existence of a bounded density and a density which is bounded away from zero on D is also discussed.

Mémoire sur l'intégration des équations aux différences partielles de la Physique mathématique.

Mathieu, Émile (1872)

Journal de Mathématiques Pures et Appliquées

Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints

Michael Hintermüller, Ian Kopacka, Stefan Volkwein (2009)

ESAIM: Control, Optimisation and Calculus of Variations

Optimal control problems for the heat equation with pointwise bilateral control-state constraints are considered. A locally superlinearly convergent numerical solution algorithm is proposed and its mesh independence is established. Further, for the efficient numerical solution reduced space and Schur complement based preconditioners are proposed which take into account the active and inactive set structure of the problem. The paper ends by numerical tests illustrating our theoretical findings and...