Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM


Autoria(s): Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria; Schwab, Christophe
Data(s)

01/02/2014

Resumo

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, 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 square root 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 cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

Formato

text

Identificador

http://centaur.reading.ac.uk/36000/1/m2an---revised-black.pdf

Hiptmair, R., Moiola, A. <http://centaur.reading.ac.uk/view/creators/90005242.html>, Perugia, I. and Schwab, C. (2014) Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM. ESAIM: Mathematical Modelling and Numerical Analysis M2AN, 48 (3). pp. 727-752. ISSN 1290-3841 doi: 10.1051/m2an/2013137 <http://dx.doi.org/10.1051/m2an/2013137>

Idioma(s)

en

Publicador

EDP Sciences

Relação

http://centaur.reading.ac.uk/36000/

creatorInternal Moiola, Andrea

http://dx.doi.org/10.1051/m2an/2013137

10.1051/m2an/2013137

Tipo

Article

PeerReviewed