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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Adjoint-based anisotropic hp-adaptation for discontinuous Galerkin methods using a continuous mesh model
Original language description
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.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA17-01747S" target="_blank" >GA17-01747S: Theory and numerical analysis of coupled problems in fluid dynamics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)