Algebraic and Discretization Error Estimation by Equilibrated Fluxes for Discontinuous Galerkin Methods on Nonmatching Grids

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10301814" target="_blank" >RIV/00216208:11320/15:10301814 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10915-014-9921-2" target="_blank" >http://dx.doi.org/10.1007/s10915-014-9921-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10915-014-9921-2" target="_blank" >10.1007/s10915-014-9921-2</a>

Result language
angličtina
Original language name
Algebraic and Discretization Error Estimation by Equilibrated Fluxes for Discontinuous Galerkin Methods on Nonmatching Grids
Original language description
We derive a posteriori error estimates for the discontinuous Galerkin method applied to the Poisson equation. We allow for a variable polynomial degree and simplicial meshes with hanging nodes and propose an approach allowing for simple (nonconforming) flux reconstructions in such a setting. We take into account the algebraic error stemming from the inexact solution of the associated linear systems and propose local stopping criteria for iterative algebraic solvers. An algebraic error flux reconstruction is introduced in this respect. Guaranteed reliability and local efficiency are proven. We next propose an adaptive strategy combining both adaptive mesh refinement and adaptive stopping criteria. At last, we detail a form of the estimates avoiding anypractical reconstruction of a flux and only working with the approximate solution, which simplifies greatly their evaluation. Numerical experiments illustrate a tight control of the overall error, good prediction of the distribution of bo
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GA13-00522S" target="_blank" >GA13-00522S: Qualitative analysis and numerical solution of problems of flows in generally time-dependent domains with various boundary conditions</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)