English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We propose a second-order total generalized variation (TGV) regularizationfor the reconstruction of the initial condition in variational dataassimilation problems. After showing the equivalence between TGV regularizationand the Bayesian method for the MAP estimator, we focus on the detailed studyof the inviscid Burgers' data assimilation problem. Due to the difficultstructure of the governing hyperbolic conservation law, we consider adiscretize-then-optimize approach and derive first-order optimality conditionsfor the problem. For the numerical solution, we propose a globalized reducedNewton-type method and prove convergence of the algorithm to stationary points.The paper finishes with some numerical experiments where among others, theperformance of TGV-regularization compared to the TV-regularization is tested.

Total Generalized Variation Regularization in Variational Data Assimilation for Burgers' Equation