Stability of the $L^2$-projection
A talk in the BI.discrete Workshop series by
Tabea Tscherpel from Bielefeld
| Abstract: | The $L^2$-projection mapping to Lagrange finite element spaces is a useful tool in numerical analysis. For adaptively generated meshes the proof of Sobolev stability is challenging and assumptions on the grading are unavoidable. We present recent results on $L^p$ and $W^{1,p}$-stability in 2D and 3D for any polynomial degree and for any space dimension under suitable conditions on the mesh grading. This includes $W^{1,2}$-stability in 2D for any polynomial degree and meshes generated by newest vertex bisection. Under realistic but conjectured assumptions on the mesh grading in 3D we show $W^{1,2}$-stability for all polynomial degrees. This is joint work with Lars Diening and Johannes Storn from Bielefeld University (Germany). Attendance is only possible after registration with the organizers and with 3G-certificate. Within the CRC this talk is associated to the project(s): A7, B7 |