hp-ADAPTATION DRIVEN BY POLYNOMIAL-DEGREE-ROBUST A POSTERIORI ERROR ESTIMATES FOR ELLIPTIC PROBLEMS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10330313" target="_blank" >RIV/00216208:11320/16:10330313 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1137/15M1026687" target="_blank" >http://dx.doi.org/10.1137/15M1026687</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/15M1026687" target="_blank" >10.1137/15M1026687</a>

Jazyk výsledku

angličtina

Název v původním jazyce

hp-ADAPTATION DRIVEN BY POLYNOMIAL-DEGREE-ROBUST A POSTERIORI ERROR ESTIMATES FOR ELLIPTIC PROBLEMS

Popis výsledku v původním jazyce

We devise and study experimentally adaptive strategies driven by a posteriori error estimates to select automatically both the space mesh and the polynomial degree in the numerical approximation of diffusion equations in two space dimensions. The adaptation is based on equilibrated flux estimates. These estimates are presented here for inhomogeneous Dirichlet and Neumann boundary conditions, for spatially varying polynomial degree, and for mixed rectangular-triangular grids possibly containing hanging nodes. They deliver a global error upper bound with constant one and, up to data oscillation, error lower bounds on element patches with a generic constant dependent only on the mesh regularity and with a computable bound. We numerically assess the estimates and several hp-adaptive strategies using the interior penalty discontinuous Galerkin method. Asymptotic exactness is observed for all the symmetric, nonsymmetric (odd degrees), and incomplete variants on nonnested unstructured triangular grids for a smooth solution and uniform refinement. Exponential convergence rates are reported on nonmatching triangular grids for the incomplete version on several benchmarks with a singular solution and adaptive refinement.

Název v anglickém jazyce

hp-ADAPTATION DRIVEN BY POLYNOMIAL-DEGREE-ROBUST A POSTERIORI ERROR ESTIMATES FOR ELLIPTIC PROBLEMS

Popis výsledku anglicky

We devise and study experimentally adaptive strategies driven by a posteriori error estimates to select automatically both the space mesh and the polynomial degree in the numerical approximation of diffusion equations in two space dimensions. The adaptation is based on equilibrated flux estimates. These estimates are presented here for inhomogeneous Dirichlet and Neumann boundary conditions, for spatially varying polynomial degree, and for mixed rectangular-triangular grids possibly containing hanging nodes. They deliver a global error upper bound with constant one and, up to data oscillation, error lower bounds on element patches with a generic constant dependent only on the mesh regularity and with a computable bound. We numerically assess the estimates and several hp-adaptive strategies using the interior penalty discontinuous Galerkin method. Asymptotic exactness is observed for all the symmetric, nonsymmetric (odd degrees), and incomplete variants on nonnested unstructured triangular grids for a smooth solution and uniform refinement. Exponential convergence rates are reported on nonmatching triangular grids for the incomplete version on several benchmarks with a singular solution and adaptive refinement.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal of Scientific Computing

ISSN

1064-8275

e-ISSN

—

Svazek periodika

38

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

"A3220"-"A3246"

Kód UT WoS článku

000387347700072

EID výsledku v databázi Scopus

2-s2.0-84994104700