A posteriori error analysis for elliptic pdes on domains with complicated structures

@article{Carstensen2004APE,
  title={A posteriori error analysis for elliptic pdes on domains with complicated structures},
  author={Carsten Carstensen and Stefan A. Sauter},
  journal={Numerische Mathematik},
  year={2004},
  volume={96},
  pages={691-721}
}
The discretisation of boundary value problems on complicated domains cannot resolve all geometric details such as small holes or pores. The model problem of this paper consists of a triangulated polygonal domain with holes of a size of the mesh-width at most and mixed boundary conditions for the Poisson equation. Reliable and efficient a posteriori error estimates are presented for a fully numerical discretisation with conforming piecewise affine finite elements. Emphasis is on technical… CONTINUE READING