Analysis of the FEM and DGM for an elliptic problem with a nonlinear Newton boundary condition

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10371028" target="_blank" >RIV/00216208:11320/17:10371028 - isvavai.cz</a>
Result on the web
<a href="http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/equadiff/" target="_blank" >http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/equadiff/</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Analysis of the FEM and DGM for an elliptic problem with a nonlinear Newton boundary condition
Original language description
The paper is concerned with the numerical analysis of an elliptic equation in a polygon with a nonlinear Newton boundary condition, discretized by the finite element or discontinuous Galerkin methods. Using the monotone operator theory, it is possible to prove the existence and uniqueness of the exact weak solution and the approximate solution. The main attention is paid to the study of error estimates. To this end, the regularity of the weak solution is investigated and it is shown that due to the boundary corner points, the solution looses regularity in a vicinity of these points. It comes out that the error estimation depends essentially on the opening angle of the corner points and on the parameter defining the nonlinear behaviour of the Newton boundary condition. Theoretical results are compared with numerical experiments confirming a nonstandard behaviour of error estimates.
Czech name
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Czech description
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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
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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