184 research outputs found
Intrinsic finite element modeling of a linear membrane shell problem
A Galerkin finite element method for the membrane elasticity problem on a
meshed surface is constructed by using two-dimensional elements extended into
three dimensions. The membrane finite element model is established using the
intrinsic approach suggested by [Delfour and Zol\'esio, A boundary differential
equation for thin shells. J. Differential Equations, 119(2):426--449, 1995]
A stabilized cut finite element method for partial differential equations on surfaces: The Laplace-Beltrami operator
We consider solving the Laplace-Beltrami problem on a smooth two dimensional
surface embedded into a three dimensional space meshed with tetrahedra. The
mesh does not respect the surface and thus the surface cuts through the
elements. We consider a Galerkin method based on using the restrictions of
continuous piecewise linears defined on the tetrahedra to the surface as trial
and test functions.
The resulting discrete method may be severely ill-conditioned, and the main
purpose of this paper is to suggest a remedy for this problem based on adding a
consistent stabilization term to the original bilinear form. We show optimal
estimates for the condition number of the stabilized method independent of the
location of the surface. We also prove optimal a priori error estimates for the
stabilized method
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