Volume 16, Issue 6
Using P-Refinement to Increase Boundary Derivative Convergence Rates

David Wells and Jeffrey Banks

Int. J. Numer. Anal. Mod., 16 (2019), pp. 891-924.

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  • Abstract

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.

  • History

Published online: 2019-08

  • AMS Subject Headings

65N15, 65N30

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