Interior Maximum-norm Estimates for Finite Element Methods, Part Ii
نویسندگان
چکیده
We consider bilinear forms A(-, •) connected with second-order elliptic problems and assume that for uh in a finite element space S¡,, we have A(u U),, x) = F(x) for x m Sh with local compact support. We give local estimates for u Uf, in L^ and W^ of the type "local best approximation plus weak outside influences plus the local size of F ".
منابع مشابه
Sharp estimates for finite element approximations to elliptic problems with Neumann boundary data of low regularity
Consider a second order homogeneous elliptic problem with smooth coefficients, Au = 0, on a smooth domain, Ω, but with Neumann boundary data of low regularity. Interior maximum norm error estimates are given for C0 finite element approximations to this problem. When the Neumann data is not in L1(∂Ω), these local estimates are not of optimal order but are nevertheless shown to be sharp. A method...
متن کاملFinite element error estimates on the boundary with application to optimal control
In this talk we consider a priori error estimates for an elliptic linear-quadratic Neumann boundary control problem with pointwise inequality constraints on the control. The domain is assumed to be polygonal and maybe non-convex. For discretizing the state linear finite elements are used, the control is approximated by piecewise constant ansatz functions. Approximations of the optimal control o...
متن کاملMaximum-norm Stability, Smoothing and Resolvent Estimates for Parabolic Finite Element Equations
We survey work on stability and smoothing estimates in maximum-norm for spatially semidiscrete finite element approximations of a model parabolic equation, and related such estimates for the resolvent of the corresponding discrete elliptic operator. We end with a short discussion of stability of fully discrete time stepping methods. Résumé. Nous présentons un bilan des résultats sur la stabilit...
متن کاملA second-order overlapping Schwarz method for a 2D singularly perturbed semilinear reaction-diffusion problem
An overlapping Schwarz domain decomposition is applied to a semilinear reaction-diffusion equation posed in a smooth two-dimensional domain. The problem may exhibit multiple solutions; its diffusion parameter ε2 is arbitrarily small, which induces boundary layers. The Schwarz method invokes a boundary-layer subdomain and an interior subdomain, the narrow subdomain overlap being of width O(ε| ln...
متن کاملFINITE ELEMENT CENTER PREPRINT 2000–12 APosteriori Error Analysis in themaximumnorm for a penalty finite element method for the time- dependent obstacle problem
A Posteriori Error Analysis in the maximum norm for a penalty finite element method for the time-dependent obstacle problem Abstract. We consider nite element approximation of the parabolic obstacle problem. The analysis is based on a penalty formulation of the problem where the penalisation parameter is allowed to vary in space and time. We estimate the penalisation error in terms of the penal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010