We consider Poisson's equation with a finite number of weighted Dirac masses as a source term, together with its discretization by means of conforming finite elements. For the error in fractional Sobolev spaces, we propose residual-type a posteriori estimators with a specifically tailored oscillation and show that, on two-dimensional polygonal domains, they are reliable and locally efficient. In numerical tests, their use in an adaptive algorithm leads to optimal error decay rates.
A posteriori error estimates with point sources in fractional sobolev spaces / F.D. Gaspoz, P. Morin, A. Veeser. - In: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0749-159X. - (2016). [Epub ahead of print] [10.1002/num.22065]
A posteriori error estimates with point sources in fractional sobolev spaces
A. VeeserUltimo
2016
Abstract
We consider Poisson's equation with a finite number of weighted Dirac masses as a source term, together with its discretization by means of conforming finite elements. For the error in fractional Sobolev spaces, we propose residual-type a posteriori estimators with a specifically tailored oscillation and show that, on two-dimensional polygonal domains, they are reliable and locally efficient. In numerical tests, their use in an adaptive algorithm leads to optimal error decay rates.File | Dimensione | Formato | |
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