%0 Journal Article %1 gaspoz2016optimal %A Gaspoz, Fernando D. %A Heine, Claus-Justus %A Siebert, Kunibert G. %D 2016 %J IMA Journal of Numerical Analysis %K from:mhartmann ians imported vorlaeufig %N 3 %P 1217--1241 %R 10.1093/imanum/drv044 %T Optimal Grading of the Newest Vertex Bisection and H1-Stability of the L2-Projection %U /brokenurl# + http://dx.doi.org/10.1093/imanum/drv044 %V 36 %X We show for adaptive triangulations in 2d, which are generated by the Newest Vertex Bisection, an optimal grading estimate. Roughly speaking, we construct from the piecewise constant mesh-size function a regularized one with the following two properties. First, the two functions are equivalent, and second, the regularized mesh-size function diers at most by a factor of 2 on neighboring elements. In combination with 1 this optimal grading estimate enables us to show that the L2-orthogonal projections onto the space of continuous Lagrange nite elements up to order twelve is H1-stable. We extend these results to a modied Red-Green-Renement.

@article{gaspoz2016optimal, abstract = {We show for adaptive triangulations in 2d, which are generated by the Newest Vertex Bisection, an optimal grading estimate. Roughly speaking, we construct from the piecewise constant mesh-size function a regularized one with the following two properties. First, the two functions are equivalent, and second, the regularized mesh-size function diers at most by a factor of 2 on neighboring elements. In combination with [1] this optimal grading estimate enables us to show that the L2-orthogonal projections onto the space of continuous Lagrange nite elements up to order twelve is H1-stable. We extend these results to a modied Red-Green-Renement.}, added-at = {2018-07-20T10:54:59.000+0200}, author = {Gaspoz, Fernando D. and Heine, Claus-Justus and Siebert, Kunibert G.}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/244af147514bed36522b14dfbc56d3414/mathematik}, doi = {10.1093/imanum/drv044}, interhash = {bbfc028ffff7250d752a210537bcf76b}, intrahash = {44af147514bed36522b14dfbc56d3414}, journal = {IMA Journal of Numerical Analysis}, keywords = {from:mhartmann ians imported vorlaeufig}, number = 3, owner = {alkaemper}, pages = {1217--1241}, timestamp = {2019-12-18T14:37:55.000+0100}, title = {Optimal Grading of the Newest Vertex Bisection and H1-Stability of the L2-Projection}, url = {/brokenurl# + http://dx.doi.org/10.1093/imanum/drv044}, volume = 36, year = 2016 }