Can I read Accuracy Controlled Data Assimilation for Parabolic Problems on EtoBox?

Accuracy Controlled Data Assimilation for Parabolic Problems by Dahmen, Wolfgang; Stevenson, Rob; Westerdiep, Jan is a scholarly article available to read on EtoBox.

What is Accuracy Controlled Data Assimilation for Parabolic Problems about?

This paper is concerned with the recovery of (approximate) solutions to parabolic problems from incomplete and possibly inconsistent observational data, given on a time-space cylinder that is a strict subset of the computational domain under consideration. Unlike previous approaches to this and related problems our starting point is a regularized least squares formulation in a continuous infinite-dimensional setting that is based on stable variational time-space formulations of the parabolic PDE. This allows us to derive a priori as well as a posteriori error bounds for the recovered states with respect to a certain reference solution. In these bounds the regularization parameter is disentangled from the underlying discretization. An important ingredient for the derivation of a posteriori bounds is the construction of suitable Fortin operators which allow us to control oscillation errors stemming from the discretization of dual norms. Moreover, the variational framework allows us to contrive preconditioners for the discrete problems whose application can be performed in linear time, and for which the condition numbers of the preconditioned systems are uniformly proportional to that

Author

Dahmen, Wolfgang; Stevenson, Rob; Westerdiep, Jan

Published

2021

Language

EN