Virtual Element Method for the Laplace-Beltrami equation on surfaces
نویسندگان
چکیده
منابع مشابه
An Adaptive Finite Element Method for the Laplace-Beltrami Operator on Implicitly Defined Surfaces
We present an adaptive finite element method for approximating solutions to the Laplace-Beltrami equation on surfaces in R3 which may be implicitly represented as level sets of smooth functions. Residual-type a posteriori error bounds which show that the error may be split into a “residual part” and a “geometric part” are established. In addition, implementation issues are discussed and several...
متن کاملPRELIMINARY VERSION Finite elements for the Laplace-Beltrami equation on parametric surfaces
In this paper we make a thorough study of the use of the finite element method to numerically compute harmonic maps from parametric surfaces to the plane. There are essentially two choices to be made in the FE method: (1) which elements and (2) which quadrature. We show that by using linear elements and point-based linear quadrature the method reduces to the cotangent method studied by Dziuk, P...
متن کاملThe Laplace-Beltrami operator on surfaces with axial symmetry
The physical situation which has initiated this research is that of a dielectric particle with electric charges on its surface, placed in electric field. Here, the diffusion equation of the charges is coupled with the Maxwell equations. There is an analytical solution of this system of equation [1] which involves some functional calculus with operators, in particular with Laplace-Beltrami opera...
متن کاملAnalysis of the Finite Element Method for the Laplace–Beltrami Equation on Surfaces with Regions of High Curvature Using Graded Meshes
We derive error estimates for the piecewise linear finite element approximation of the Laplace–Beltrami operator on a bounded, orientable, C3, surface without boundary on general shape regular meshes. As an application, we consider a problem where the domain is split into two regions: one which has relatively high curvature and one that has low curvature. Using a graded mesh we prove error esti...
متن کاملConvergence of the point integral method for Laplace–Beltrami equation on point cloud
The Laplace–Beltrami operator, a fundamental object associated with Riemannian manifolds, encodes all intrinsic geometry of manifolds and has many desirable properties. Recently, we proposed the point integral method (PIM), a novel numerical method for discretizing the Laplace–Beltrami operator on point clouds (Li et al. in Commun Comput Phys 22(1):228–258, 2017). In this paper, we analyze the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ESAIM: Mathematical Modelling and Numerical Analysis
سال: 2018
ISSN: 0764-583X,1290-3841
DOI: 10.1051/m2an/2017040