Finite element approximation of the Laplace–Beltrami operator on a surface with boundary
نویسندگان
چکیده
منابع مشابه
Finite-Element Approximation of Elliptic Equations with a Neumann or Robin Condition on a Curved Boundary
This paper considers a finite-element approximation of a second-order selfadjoint elliptic equation in a region flcR" (with n = 2 or 3) having a curved boundary dQ on which a Neumann or Robin condition is prescribed. If the finite-element space denned over D, a union of elements, has approximation power h in the L norm, and if the region of integration is approximated by Q* with dist (Q, £?*) =...
متن کاملFinite element approximation of fractional order elliptic boundary value problems
A finite element numerical method is investigated for fractional order elliptic boundary value problems with homogeneous Dirichlet type boundary conditions. It is pointed out that an appropriate stiffness matrix can be obtained by taking the prescribed fractional power of the stiffness matrix corresponding to the non-fractional elliptic operators. It is proved that this approach, which is also ...
متن کاملEvaluation of Fracture Parameters by Coupling the Edge-Based Smoothed Finite Element Method and the Scaled Boundary Finite Element Method
This paper presents a technique to evaluate the fracture parameters by combining the edge based smoothed finite element method (ESFEM) and the scaled boundary finite element method (SBFEM). A semi-analytical solution is sought in the region close to the vicinity of the crack tip using the SBFEM, whilst, the ESFEM is used for the rest of the domain. As both methods satisfy the partition of unity...
متن کاملFinite element approximation of spectral problems with Neumann boundary conditions on curved domains
This paper deals with the finite element approximation of the spectral problem for the Laplace equation with Neumann boundary conditions on a curved nonconvex domain Ω. Convergence and optimal order error estimates are proved for standard piecewise linear continuous elements on a discrete polygonal domain Ωh 6⊂ Ω in the framework of the abstract spectral approximation theory.
متن کاملAnalysis of a Robust Finite Element Approximation for a Parabolic Equation with Rough Boundary Data
The approximation of parabolic equations with nonhomogeneous Dirichlet boundary data by a numerical method that consists of finite elements for the space discretization and the backward Euler time discretization is studied. The boundary values are assumed in a least squares sense. It is shown that this method achieves an optimal rate of convergence for rough (only L1) boundary data and for smoo...
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: Numerische Mathematik
سال: 2018
ISSN: 0029-599X,0945-3245
DOI: 10.1007/s00211-018-0990-2