Error Estimates for the Finite Volume Element Method for Elliptic Pde’s in Nonconvex Polygonal Domains
نویسنده
چکیده
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.
منابع مشابه
Error Estimates for a Finite Volume Element Method for Elliptic PDEs 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 H1-, L2and L∞-norms, taking into consideration the regularity of the data. Numerical experiments and counterexamples illustrate the theoretical results.
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 کاملLocal a posteriori estimates for pointwise gradient errors in finite element methods for elliptic problems
We prove local a posteriori error estimates for pointwise gradient errors in finite element methods for a second-order linear elliptic model problem. First we split the local gradient error into a computable local residual term and a weaker global norm of the finite element error (the “pollution term”). Using a mesh-dependent weight, the residual term is bounded in a sharply localized fashion. ...
متن کاملFinite Volume Methods for Elliptic Pde’s: a New Approach
We consider a new formulation for finite volume element methods, which is satisfied by known finite volume methods and it can be used to introduce new ones. This framework results by approximating the test function in the formulation of finite element method. We analyze piecewise linear conforming or nonconforming approximations on nonuniform triangulations and prove optimal order H1−norm and L...
متن کاملA finite volume element method for a non-linear elliptic problem
We consider a finite volume discretization of second order nonlinear elliptic boundary value problems on polygonal domains. For sufficiently small data, we show existence and uniqueness of the finite volume solution using a fixed point iteration method. We derive error estimates in H–, L2– and L∞– norm. In addition a Newton’s method is analyzed for the approximation of the finite volume solutio...
متن کامل