English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This part contains new pointwise error estimates for the nite element method for second order elliptic boundary value problems on smooth bounded domains in RN. In a sense to be discussed below these sharpen known quasi{optimal L1 and W 1 1 estimates for the error on irregular quasi{uniform meshes in that they indicate a more local dependence of the error at a point on the derivatives of the solution u. We note that in general the higher order nite element spaces exhibit more local behavior than lower order spaces. As a consequence of these estimates new types of error expansions will be derived which are in the form of inequalities. These expansion inequalities are valid for large classes of nite elements dened on irregular grids in RN and have applications to superconvergence and extrapolation and a posteriori estimates. Part II of this series will contain local estimates applicable to non{smooth problems.

Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids: Part I. Global estimates