Quadrature approximation of one singular integral operator.
Quadrature method for singular integral equations on closed curves.
Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods
One of the main tools in the proof of residual-based a posteriori error estimates is a quasi-interpolation operator due to Clément. We modify this operator in the setting of a partition of unity with the effect that the approximation error has a local average zero. This results in a new residual-based a posteriori error estimate with a volume contribution which is smaller than in the standard estimate. For an elliptic model problem, we discuss applications to conforming, nonconforming and mixed...