Girke, Stefan; Klöfkorn, Robert; Ohlberger, Mario Efficient parallel simulation of atherosclerotic plaque formation using higher order discontinuous Galerkin schemes. (English) Zbl 1326.92035 Fuhrmann, Jürgen (ed.) et al., Finite volumes for complex applications VII – elliptic, parabolic and hyperbolic problems. Proceedings of the FVCA 7, Berlin, Germany, June 15–20, 2014. Vol. II. Cham: Springer (ISBN 978-3-319-05590-9/hbk; 978-3-319-05591-6/ebook; 978-3-319-06402-4/set). Springer Proceedings in Mathematics & Statistics 78, 617-625 (2014). Summary: The compact discontinuous Galerkin 2 (CDG2) method was successfully tested for elliptic problems, scalar convection-diffusion equations and compressible Navier-Stokes equations. In this paper we use the newly developed DG method to solve a mathematical model for early stages of atherosclerotic plaque formation. Atherosclerotic plaque is mainly formed by accumulation of lipid-laden cells in the arterial walls which leads to a heart attack in case the artery is occluded or a thrombus is built through a rupture of the plaque. After describing a mathematical model and the discretization scheme, we present some benchmark tests comparing the CDG2 method to other commonly used DG methods. Furthermore, we take parallelization and higher order discretization schemes into account.For the entire collection see [Zbl 1291.65005]. Cited in 1 Document MSC: 92C50 Medical applications (general) 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65Y05 Parallel numerical computation PDFBibTeX XMLCite \textit{S. Girke} et al., Springer Proc. Math. Stat. 78, 617--625 (2014; Zbl 1326.92035) Full Text: DOI arXiv