A continuous hp-mesh model for adaptive discontinuous Galerkin schemes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384597" target="_blank" >RIV/00216208:11320/18:10384597 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S016892741730209X?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S016892741730209X?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.apnum.2017.09.015" target="_blank" >10.1016/j.apnum.2017.09.015</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A continuous hp-mesh model for adaptive discontinuous Galerkin schemes

Popis výsledku v původním jazyce

We present a continuous-mesh model for anisotropic hp-adaptation in the context of numerical methods using discontinuous piecewise polynomial approximation spaces. The present work is an extension of a previously proposed mesh-only (h-)adaptation method which uses both a continuous mesh, and a corresponding high-order continuous interpolation operator. In this previous formulation local anisotropy and global mesh density distribution may be determined by analytical optimization techniques, operating on the continuous mesh model. The addition of varying polynomial degree necessitates a departure from purely analytic optimization. However, we show in this article that a global optimization problem may still be formulated and solved by analytic optimization, adding only the necessity to solve numerically a single nonlinear algebraic equation per adaptation step to satisfy a constraint on the total number of degrees of freedom. The result is a tailorsuited continuous mesh with respect to a model for the global interpolation error measured in the Lq-norm. From the continuous mesh a discrete triangular mesh may be generated using any metric-based mesh generator.

Název v anglickém jazyce

A continuous hp-mesh model for adaptive discontinuous Galerkin schemes

Popis výsledku anglicky

We present a continuous-mesh model for anisotropic hp-adaptation in the context of numerical methods using discontinuous piecewise polynomial approximation spaces. The present work is an extension of a previously proposed mesh-only (h-)adaptation method which uses both a continuous mesh, and a corresponding high-order continuous interpolation operator. In this previous formulation local anisotropy and global mesh density distribution may be determined by analytical optimization techniques, operating on the continuous mesh model. The addition of varying polynomial degree necessitates a departure from purely analytic optimization. However, we show in this article that a global optimization problem may still be formulated and solved by analytic optimization, adding only the necessity to solve numerically a single nonlinear algebraic equation per adaptation step to satisfy a constraint on the total number of degrees of freedom. The result is a tailorsuited continuous mesh with respect to a model for the global interpolation error measured in the Lq-norm. From the continuous mesh a discrete triangular mesh may be generated using any metric-based mesh generator.

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

2018

Kód důvěrnosti údajů

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

Název periodika

Applied Numerical Mathematics

ISSN

0168-9274

e-ISSN

—

Svazek periodika

124

Číslo periodika v rámci svazku

February 2018

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

21

Strana od-do

1-21

Kód UT WoS článku

000417668200001

EID výsledku v databázi Scopus

2-s2.0-85030834163