In Part I of this work, we develop superconvergence estimates for piecewise linear finite element approximations on quasi-uniform triangular meshes where most pairs of triangles sharing a common edge form approximate parallelograms. In particular, we first show a superconvergence of the gradient of the finite element solution u h and to the gradient of the interpolant u I, We then analyze a postprocessing gradient recovery scheme, showing that Q h∇u h is superconvergent approximation to ∇u. Here Q h is the global L 2 projection. In Part II, we analyze a superconvergent gradient recovery scheme for general unstructured, shape regular triangulations. This is the foundation for an a posteriori error estimate and local error indicators.
|Original language||English (US)|
|Number of pages||19|
|Journal||SIAM Journal on Numerical Analysis|
|State||Published - Dec 1 2003|
Bibliographical noteGenerated from Scopus record by KAUST IRTS on 2023-02-15
ASJC Scopus subject areas
- Numerical Analysis