TITLE:
Error Estimator Using Higher Order FEM for an Interface Problem
AUTHORS:
Maharavo Randrianarivony
KEYWORDS:
Estimator, A-Posteriori, Interface, Transmission, Higher Order, FEM, Residual
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.12,
December
18,
2017
ABSTRACT: A higher order finite element method is considered to treat an interface problem.
The polynomial degree is allowed to be arbitrary but it is fixed for the
FEM-variational formulation. We propose an error estimator which turns out
to be efficient and reliable. We demonstrate upper and lower bounds of the
error estimator with respect to the exact accuracy. For the transmission problem,
the coefficients for the internal and external domains can be highly dissimilar.
One major difficulty is the characteristic of the estimator at the interface.
The a-posteriori error estimates can be computed very efficiently element
by element. To corroborate the theoretical analysis, we report on a few
numerical results.