A cut discontinuous Galerkin method for the Laplace–Beltrami operator
2017 (English)In: IMA Journal of Numerical Analysis, ISSN 0272-4979, E-ISSN 1464-3642, Vol. 37, no 1, 138-169 p.Article in journal (Refereed) Published
We develop a discontinuous cut finite element method for the Laplace–Beltrami operator on a hypersurface embedded in R. The method is constructed by using a discontinuous piecewise linear finite element space defined on a background mesh in R. The surface is approximated by a continuous piecewise linear surface that cuts through the background mesh in an arbitrary fashion. Then, a discontinuous Galerkin method is formulated on the discrete surface and in order to obtain coercivity, certain stabilization terms are added on the faces between neighbouring elements that provide control of the discontinuity as well as the jump in the gradient. We derive optimal a priori error and condition number estimates which are independent of the positioning of the surface in the background mesh. Finally, we present numerical examples confirming our theoretical results.
Place, publisher, year, edition, pages
Oxford University Press, 2017. Vol. 37, no 1, 138-169 p.
Surface PDE, Laplace–Beltrami, discontinuous Galerkin, Cut finite element method
Computational Mathematics Mathematical Analysis
IdentifiersURN: urn:nbn:se:hj:diva-34834DOI: 10.1093/imanum/drv068OAI: oai:DiVA.org:hj-34834DiVA: diva2:1067744