A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
In this article we develop 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 . The theory hinges on local approximation properties of either Clément or Scott–Zhang interpolation...