@article{,
    author = {Apel, Thomas; Nicaise, Serge; Pfefferer, Johannes},
    title = {Adapted numerical methods for the numerical solution of the Poisson equation with $L^2$ boundary data in non-convex domains},
    editor = {},
    booktitle = {},
    series = {},
    journal = {SIAM Journal on Numerical Analysis},
    address = {},
    publisher = {},
    edition = {},
    year = {2017},
    isbn = {},
    volume = {55},
    number =  {4},
    pages = {1937-1957},
    url = {},
    doi = {10.1137/16M1062077},
    keywords = {},
    abstract = {The very weak solution of the Poisson equation with $L^2$ boundary data is defined by the method of transposition. The finite element solution with regularized boundary data converges in the $L^2(mega)$-norm with order $1/2$ in convex domains but has a reduced convergence order in non-convex domains although the solution remains to be contained in $H^{1/2}(mega)$. The reason is a singularity in the dual problem. In this paper we propose and analyze, as a remedy, both a standard finite element method with mesh grading and a dual variant of the singular complement method. The error order 1/2 is retained in both cases also with non-convex domains. Numerical experiments confirm the theoretical results.},
    note = {},
    institution = {Universität der Bundeswehr München, Fakultät für Bauingenieurwesen und Umweltwissenschaften, BAU 1 - Institut für Mathematik und Computergestützte Simulation, Professur: Apel, Thomas},
    
    
}