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

The focus of this work is the numerical approximation of time-dependentpartial differential equations associated to initial-boundary value problems.This master dissertation is mostly concerned with the actual computation of thesolution to nonlinear stochastic evolution problems governed byKardar-Parisi-Zhang (KPZ) models. In addition, the dissertation aims tocontribute to corroborate, by means of a large set of numerical experiments,that the initial-boundary value problem with periodic boundary conditions forthe equation KPZ is ill-posed and that such equation needs to be renormalized.The approach to discretization of KPZ equation perfomed by means of the use ofhybrid and mixed finite elements with a domain decomposition procedure alongwith a pertinent mollification of the noise. The obtained solution is comparedwith the well known solution given by the Cole-Hopf transformation of thestochastic heat equation with multiplicative noise. We were able to verify thatboth solutions exhibit a good agreement, but there is a shift that grows as thesupport of the mollifier decreases. For the numerical aproximation of thestochastic heat equation we use a state-of-the-art numerical method forevaluating semilinear stochastic PDE , which in turn combine spectraltechniques, Taylor's expantions and particular numerical treatment to theunderlying noise. Furthermore, a state-of-the-art renormalization procedureintroduced by Martin Hairer is used to renormalize KPZ equation that isvalidated with nontrivial numerical experiments.

Combined use of mixed and hybrid finite elements method with domain  decomposition and spectral methods for a study of renormalization for the KPZ  model