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We present a quick overview of the general problem to find optimal a priori and a posteriori error estimates for the approximation of dissipative evolution equations in Hilbert and metric spaces by means of a variational formulation of the implicit Euler scheme. We shall discuss what are the intrinsic metric arguments which are involved in the derivation of the estimates and we present an elementary proof in a simplified finite dimensional case. An application to the porous medium equation in the new framework of the Wasserstein distance is briefly sketched.

Error Estimates for Dissipative Evolution Problems

SAVARE', GIUSEPPE
2004-01-01

Abstract

We present a quick overview of the general problem to find optimal a priori and a posteriori error estimates for the approximation of dissipative evolution equations in Hilbert and metric spaces by means of a variational formulation of the implicit Euler scheme. We shall discuss what are the intrinsic metric arguments which are involved in the derivation of the estimates and we present an elementary proof in a simplified finite dimensional case. An application to the porous medium equation in the new framework of the Wasserstein distance is briefly sketched.
2004
Free Boundary Problems. Theory and Applications
COLLI P.; VERDI C.; VISINTIN C.
The Mathematics category includes resources dealing with mathematics, applied mathematics, statistics and probability.
WOS:000189398800022
Inglese
Internazionale
STAMPA
147
281
292
9783764321932
Birkhauser
BASEL
SVIZZERA
The book appears in the International Series of Numerical Mathematics and collects many contributions presented at the International Conference on Free Boundary Problems that took place in Trento, June 2002. Many phenomena of interest for applications are represented by differential equations which are defined in a domain whose boundary is a priori unknown, and is accordingly named a "free boundary". A further quantitative condition is then provided in order to exclude indeterminacy. Free boundary problems thus encompass a broad spectrum which is represented in this state-of-the-art volume by a variety of contributions of researchers in mathematics and applied fields like physics, biology and material sciences. Special emphasis has been reserved for mathematical modelling and for the formulation of new problems.
Gradient flows; Wasserstein distance; Dissipative evolution equations; Optimal error estimates
http://www.springer.com/birkhauser/mathematics/book/978-3-7643-2193-2
2 Contributo in Volume::2.1 Contributo in volume (Capitolo o Saggio)
1
268
none
Savare', Giuseppe
info:eu-repo/semantics/bookPart
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/124454
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