A continuous hp-mesh model for adaptive discontinuous Galerkin schemes

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
A continuous hp-mesh model for adaptive discontinuous Galerkin schemes
Original language description
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.
Czech name
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Czech description
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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
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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