期刊
IMA JOURNAL OF NUMERICAL ANALYSIS
卷 37, 期 1, 页码 138-169出版社
OXFORD UNIV PRESS
DOI: 10.1093/imanum/drv068
关键词
surface PDE; Laplace-Beltrami; discontinuous Galerkin; cut finite element method
资金
- EPSRC, UK [EP/J002313/1]
- Swedish Foundation for Strategic Research [AM13-0029]
- Swedish Research Council [2011-4992, 2013-4708]
- Swedish strategic research programme eSSENCE
- EPSRC [EP/J002313/2, EP/P01576X/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/P01576X/1, EP/J002313/2] Funding Source: researchfish
We develop a discontinuous cut finite element method for the Laplace-Beltrami operator on a hypersurface embedded in R-d. The method is constructed by using a discontinuous piecewise linear finite element space defined on a background mesh in R-d. 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.
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