On the Sobolev and L^p-Stability of the L^2-projection

by   Lars Diening, et al.

We show stability of the L^2-projection onto Lagrange finite element spaces with respect to (weighted) L^p and W^1,p-norms for any polynomial degree and for any space dimension under suitable conditions on the mesh grading. This includes W^1,2-stability in two space dimensions for any polynomial degree and meshes generated by newest vertex bisection. Under realistic assumptions on the mesh grading in three dimensions we show W^1,2-stability for all polynomial degrees greater than one. We also propose a modified bisection strategy that leads to better W^1,p-stability. Moreover, we investigate the stability of the L^2-projection onto Crouzeix-Raviart elements.



There are no comments yet.


page 1

page 2

page 3

page 4


H^1-Stability of the L^2-Projection onto Finite Element Spaces on Adaptively Refined Quadrilateral Meshes

The L^2-orthogonal projection Π_h:L^2(Ω)→𝕍_h onto a finite element (FE) ...

On the stability of the L^2 projection and the quasiinterpolant in the space of smooth periodic splines

In this paper we derive stability estimates in L^2- and L^∞- based Sobol...

Global and local pointwise error estimates for finite element approximations to the Stokes problem on convex polyhedra

The main goal of the paper is to show new stability and localization res...

A tropical geometry approach to BIBO stability

Given a Laurent polynomial F and its amoeba AF. We relate here the quest...

Critical Functions and Inf-Sup Stability of Crouzeix-Raviart Elements

In this paper, we prove that Crouzeix-Raviart finite elements of polynom...

Dimension of polynomial splines of mixed smoothness on T-meshes

In this paper we study the dimension of splines of mixed smoothness on a...

A simple history dependent remeshing technique to increase finite element model stability in elastic surface deformations

In this paper, we present and validate a simple adaptive surface remeshi...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.