The shifted boundary method for embedded domain computations. Part I: Poisson and Stokes problems

Published

Journal Article

© 2017 Elsevier Inc. We propose a new finite element method for embedded domain computations, which falls in the category of surrogate/approximate boundary algorithms. The key feature of the proposed approach is the idea of shifting the location where boundary conditions are applied from the true to the surrogate boundary, and to appropriately modify the shifted boundary conditions, enforced weakly, in order to preserve optimal convergence rates of the numerical solution. This process yields a method which, in our view, is simple, efficient, and also robust, since it is not affected by the small-cut-cell problem. Although general in nature, here we apply this new concept to the Poisson and Stokes problems. We present in particular the full analysis of stability and convergence for the case of the Poisson operator, and numerical tests for both the Poisson and Stokes equations, for geometries of progressively higher complexity.

Full Text

Duke Authors

Cited Authors

  • Main, A; Scovazzi, G

Published Date

  • November 1, 2018

Published In

Volume / Issue

  • 372 /

Start / End Page

  • 972 - 995

Electronic International Standard Serial Number (EISSN)

  • 1090-2716

International Standard Serial Number (ISSN)

  • 0021-9991

Digital Object Identifier (DOI)

  • 10.1016/j.jcp.2017.10.026

Citation Source

  • Scopus