Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-DGFEM
Open access
Datum
2012-11Typ
- Report
ETH Bibliographie
yes
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Abstract
We study the approximation of harmonic functions by means of harmonic polynomials in twodimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a $\delta$-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on $\delta$. We apply the obtained estimates to show exponential convergence with rate $O(exp(-b\sqrt{N}))$, $N$ being the number of degrees of freedom and $b > 0$, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate $O(exp(-b \sqrt[3]{N}))$, and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces. Mehr anzeigen
Persistenter Link
https://doi.org/10.3929/ethz-a-010392193Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
SAM Research ReportBand
Verlag
Seminar for Applied Mathematics, ETH ZurichOrganisationseinheit
03435 - Schwab, Christoph / Schwab, Christoph
03632 - Hiptmair, Ralf / Hiptmair, Ralf
Förderung
247277 - Automated Urban Parking and Driving (EC)
Zugehörige Publikationen und Daten
Is previous version of: http://hdl.handle.net/20.500.11850/78110
ETH Bibliographie
yes
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