A discontinuous Galerkin Nitsche method for elliptic problems with fictitious boundary
(English)Manuscript (preprint) (Other academic)
We present a discountinous Galerkin method, based on the classical method of Nitsche, for elliptic problems with an immersed boundary representation on a structured grid. In such methods very small elements typically occur at the boundary, leading to breakdown of the discrete coercivity as well as numerical instabilities. In this work we propose a method that avoids using very small elements on the boundary by associating them to a neighboring element with a sufficiently large intersection with the domain. This construction allows us to prove the crucial inverse inequality that leads to a coercive bilinear form and as a consequence we obtain optimal order a priori error estimates. We also discuss the implementation of the method and present a numerical example in three dimensions.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:umu:diva-33868OAI: oai:DiVA.org:umu-33868DiVA: diva2:318485