2013/07/03 by Michael Karkulik, Karkulik, Michael, Carl‐Martin Pfeiler +3
Computer Science · Engineering · Mathematics · #65N30 #65N50 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical Analysis (math.NA) #Numerical methods in engineering #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1307.0917
openalex publication_date 2013/07/03 · openalex created_date 2022/09/29 · openalex updated_date 2026/07/28
We merge and extend recent results which prove the H1-stability of the\nL2-orthogonal projection onto standard finite element spaces, provided that the\nunderlying simplicial triangulation is appropriately graded. For lowest-order\nCourant finite elements S1(T) in Rd with d>=2, we prove that such a grading is\nalways ensured for adaptive meshes generated by newest vertex bisection. For\nhigher-order finite elements Sp(T) with p>=1, we extend existing bounds on the\npolynomial degree with a computer-assisted proof. We also consider\nL2-orthogonal projections onto certain subspaces of Sp(T) which incorporate\nzero Dirichlet boundary conditions resp. an integral mean zero property.\n