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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
hp-ADAPTATION DRIVEN BY POLYNOMIAL-DEGREE-ROBUST A POSTERIORI ERROR ESTIMATES FOR ELLIPTIC PROBLEMS
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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