CIEM 05476
CENTRO DE INVESTIGACION Y ESTUDIOS DE MATEMATICA
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
Autor/es:
AGNELLI J.P.; GARAU E.M.; MORIN P.
Lugar:
Montevideo
Reunión:
Conferencia; Foundations of Computational Mathematics; 2014
Institución organizadora:
Universidad de la Republica
Resumen:
In this work we develop a posteriori error estimates for second order linear elliptic problems with point sources in two- and three-dimensional domains. We prove a global upper bound and a local lower bound for the error measured in a weighted Sobolev space. The weight considered is a (positive) power of the distance to the support of the Dirac delta source term, and belongs to the Muckenhoupt's class A2. The theory hinges on local approximation properties of either Clement or Scott-Zhang interpolation operators, without need of modi cations, and makes use of weighted estimates for fractional integrals and maximal functions. Numerical experiments with an adaptive algorithm yield optimal meshes and very good e ectivity indices.
