@Article{IJNAM-16-891,
author = {Wells , David and Banks , Jeffrey},
title = {Using $p$-Refinement to Increase Boundary Derivative Convergence Rates},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2019},
volume = {16},
number = {6},
pages = {891--924},
abstract = {<p style="text-align: justify;">Many important physical problems, such as fluid structure interaction or conjugate
heat transfer, require numerical methods that compute boundary derivatives or fluxes to high accuracy. This paper proposes a novel approach to calculating accurate approximations of boundary
derivatives of elliptic problems. We describe a new continuous finite element method based on $p$-refinement of cells adjacent to the boundary that increases the local degree of the approximation. We prove that the order of the approximation on the $p$-refined cells is, in 1D, determined
by the rate of convergence at the mesh vertex connecting the higher and lower degree cells and
that this approach can be extended, in a restricted setting, to 2D problems. The proven convergence rates are numerically verified by a series of experiments in both 1D and 2D. Finally, we
demonstrate, with additional numerical experiments, that the $p$-refinement method works in more
general geometries.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/13259.html}
}