A posteriori error estimates with point sources in fractional Sobolev\n spaces

2015/07/29 by Fernando Gaspoz, Gaspoz, Fernando D., Pedro Morín +3
Mathematics · Computer Science · Engineering · #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics

paper · pdf · doi:10.48550/arxiv.1507.08247

Abstract

We consider Poisson's equation with a finite number of weighted Dirac masses\nas a source term, together with its discretization by means of conforming\nfinite elements. For the error in fractional Sobolev spaces, we propose\nresidual-type a posteriori estimators with a specifically tailored oscillation\nand show that, on two-dimensional polygonal domains, they are reliable and\nlocally efficient. In numerical tests, their use in an adaptive algorithm leads\nto optimal error decay rates.\n

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