Finite Element Error Estimates on Geometrically Perturbed Domains
نویسندگان
چکیده
منابع مشابه
Diffusion-uniform Error Estimates for Nonlinear Singularly Perturbed Problems in Finite Element Methods
∂n ∣∣ ΓN×(0,T ) = gN , d) u(x, 0) = u(x), x ∈ Ω. Our aim is to derive apriori error estimates in the L∞(L2)-norm which are uniform with respect to ε → 0 and are valid even for the limiting case ε = 0. In the case of linear advection-diffusion this has been done e.g. in [2]. In the nonlinear case, for various explicit time discretizations of the DG scheme, such an error analysis was presented in...
متن کاملUniform error estimates in the finite element method for a singularly perturbed reaction-diffusion problem
Consider the problem− 2∆u+u = f with homogeneous Neumann boundary condition in a bounded smooth domain in RN . The whole range 0 < ≤ 1 is treated. The Galerkin finite element method is used on a globally quasi-uniform mesh of size h; the mesh is fixed and independent of . A precise analysis of how the error at each point depends on h and is presented. As an application, first order error estima...
متن کاملError Estimates for the Finite Element Approximation of Problems in Unbounded Domains
In this paper we present error estimates for the finite element approximation of linear elliptic problems in unbounded domains that are outside an obstacle and a semi-infinite strip in the plane. The finite element approximation is formulated on a bounded domain using a nonlocal approximate artificial boundary condition. In fact there is a family of approximate boundary conditions with increasi...
متن کاملError Estimates for the Finite Volume Element Method for Parabolic Equations in Convex Polygonal Domains
We analyze the spatially semidiscrete piecewise linear finite volume element method for parabolic equations in a convex polygonal domain in the plane. Our approach is based on the properties of the standard finite element Ritz projection and also of the elliptic projection defined by the bilinear form associated with the variational formulation of the finite volume element method. Because the d...
متن کاملError Estimates for the Finite Volume Element Method for Elliptic Pde’s in Nonconvex Polygonal Domains
We consider standard finite volume piecewise linear approximations for second order elliptic boundary value problems on a nonconvex polygonal domain. Based on sharp shift estimates, we derive error estimations in H –, L2– and L∞–norm, taking into consideration the regularity of the data. Numerical experiments and counterexamples illustrate the theoretical results.
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: Journal of Scientific Computing
سال: 2020
ISSN: 0885-7474,1573-7691
DOI: 10.1007/s10915-020-01285-y