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ASYMPTOTICALLY EXACT A POSTERIORI ERROR ESTIMATORS, PART I: GRIDS WITH SUPERCONVERGENCE.
- Source :
-
SIAM Journal on Numerical Analysis . 2003, Vol. 41 Issue 6, p2294-2312. 19p. - Publication Year :
- 2003
-
Abstract
- 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 uh and to the gradient of the interpolant uI. We then analyze a postprocessing gradient recovery scheme, showing that Qh∇uh is a superconvergent approximation to ∇u. Here Qh is the global L2 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00361429
- Volume :
- 41
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Numerical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 14691907
- Full Text :
- https://doi.org/10.1137/S003614290139874X