@Article{IJNAM-13-513, author = {}, title = {A Note on Optimal Spectral Bounds for Nonoverlapping Domain Decomposition Preconditioners for Hp-Version Discontinuous Galerkin Methods}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {4}, pages = {513--524}, abstract = {In this article, we consider the derivation of hp-optimal spectral bounds for a class of domain decomposition preconditioners based on the Schwarz framework for discontinuous Galerkin finite element approximations of second-order elliptic partial differential equations. In particular, we improve the bounds derived in our earlier article [P.F. Antonietti and P. Houston, J. Sci. Comput., 46(1):124-149, 2011] in the sense that the resulting bound on the condition number of the preconditioned system is not only explicit with respect to the coarse and fine mesh sizes H and h, respectively, and the fine mesh polynomial degree p, but now also explicit with respect to the polynomial degree q employed for the coarse grid solver. More precisely, we show that the resulting spectral bounds are of order p²H/(qh) for the hp-version of the discontinuous Galerkin method.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/450.html} }