| dc.description.abstract |
Based on the analysis of Cockburn et al. [Math. Comp. 78 (2009),
pp. 1-24] for a selfadjoint linear elliptic equation, we first discuss superconvergence
results for nonselfadjoint linear elliptic problems using discontinuous
Galerkin methods. Further, we have extended our analysis to derive superconvergence
results for quasilinear elliptic problems. When piecewise polynomials
of degree k ≥ 1 are used to approximate both the potential as well as the
flux, it is shown, in this article, that the error estimate for the discrete flux in
L2-norm is of order k + 1. Further, based on solving a discrete linear elliptic
problem at each element, a suitable postprocessing of the discrete potential
is developed and then, it is proved that the resulting post-processed potential
converges with order of convergence k + 2 in L2-norm. These results confirm
superconvergent results for linear elliptic problems. |
en_US |