Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids: Part I. Global estimates

@article{Schatz1998PointwiseEE,
  title={Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids: Part I. Global estimates},
  author={Alfred H. Schatz},
  journal={Math. Comput.},
  year={1998},
  volume={67},
  pages={877-899}
}
This part contains new pointwise error estimates for the finite element method for second order elliptic boundary value problems on smooth bounded domains in RN . In a sense to be discussed below these sharpen known quasi–optimal L∞ and W 1 ∞ estimates for the error on irregular quasi–uniform meshes in that they indicate a more local dependence of the error at a point on the derivatives of the solution u. We note that in general the higher order finite element spaces exhibit more local behavior… CONTINUE READING
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