Adjoint-based anisotropic hp-adaptation for discontinuous Galerkin methods using a continuous mesh model

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10419205" target="_blank" >RIV/00216208:11320/20:10419205 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=uz_0DqZa8e" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=uz_0DqZa8e</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jcp.2020.109321" target="_blank" >10.1016/j.jcp.2020.109321</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Adjoint-based anisotropic hp-adaptation for discontinuous Galerkin methods using a continuous mesh model

Popis výsledku v původním jazyce

In this paper we propose an adjoint-based hp-adaptation method for conservation laws, and corresponding numerical schemes based on piecewise polynomial approximation spaces. The method uses a continuous mesh framework, similar to that proposed in [1], where a global optimization scheme was formulated with respect to the error in the numerical solution, measured in any L-q norm. The novelty of the present work is the extension to more general optimization targets. Here, any solution-dependent functional, which is compatible with an adjoint equation, may be the target of the continuous-mesh optimization. We present the rationale behind the formulation of the optimization problem, with particular emphasis on the continuous mesh model, and the relevant adjoint-based error estimate. Additionally we combine the adjoint-based error estimates with the polynomial optimization strategy from [2] to present a complete hp-adaptation method which shows exponential convergence in the target function. The h-only mesh adaptation strategy of this work has been presented as a conference proceeding earlier [3]. Numerical experiments are carried out to demonstrate the viability of the scheme. (C) 2020 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

Adjoint-based anisotropic hp-adaptation for discontinuous Galerkin methods using a continuous mesh model

Popis výsledku anglicky

In this paper we propose an adjoint-based hp-adaptation method for conservation laws, and corresponding numerical schemes based on piecewise polynomial approximation spaces. The method uses a continuous mesh framework, similar to that proposed in [1], where a global optimization scheme was formulated with respect to the error in the numerical solution, measured in any L-q norm. The novelty of the present work is the extension to more general optimization targets. Here, any solution-dependent functional, which is compatible with an adjoint equation, may be the target of the continuous-mesh optimization. We present the rationale behind the formulation of the optimization problem, with particular emphasis on the continuous mesh model, and the relevant adjoint-based error estimate. Additionally we combine the adjoint-based error estimates with the polynomial optimization strategy from [2] to present a complete hp-adaptation method which shows exponential convergence in the target function. The h-only mesh adaptation strategy of this work has been presented as a conference proceeding earlier [3]. Numerical experiments are carried out to demonstrate the viability of the scheme. (C) 2020 Elsevier Inc. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA17-01747S" target="_blank" >GA17-01747S: Teorie a numerická analýza sdružených problémů dynamiky tekutin</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Computational Physics

ISSN

0021-9991

e-ISSN

—

Svazek periodika

409

Číslo periodika v rámci svazku

May 15, 2020

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

23

Strana od-do

109321

Kód UT WoS článku

000522726000003

EID výsledku v databázi Scopus

2-s2.0-85080059252