Authors: Hajduk, Hennes
Kuzmin, Dmitri
Kolev, Tzanio
Tomov, Vladimir
Tomas, Ignacio
Shadid, John. N.
Title: Matrix-free subcell residual distribution for Bernstein finite elements: Monolithic limiting
Language (ISO): en
Abstract: This paper is focused on the aspects of limiting in residual distribution (RD) schemes for high-order finite element approximations to advection problems. Both continuous and discontinuous Galerkin methods are considered in this work. Discrete maximum principles are enforced using algebraic manipula-tions of element contributions to the global nonlinear system. The required modifications can be carried out without calculating the element matrices and assembling their global counterparts. The components of element vec-tors associated with the standard Galerkin discretization are manipulated di-rectly using localized subcell weights to achieve optimal accuracy. Low-order nonlinear RD schemes of this kind were originally developed to calculate local extremum diminishing predictors for flux-corrected transport (FCT) algorithms. In the present paper, we incorporate limiters directly into the residual distribution procedure, which makes it applicable to stationary prob-lems and leads to well-posed nonlinear discrete problems. To circumvent the second-order accuracy barrier, the correction factors of monolithic limiting approaches and FCT schemes are adjusted using smoothness sensors based on second derivatives. The convergence behavior of presented methods is illustrated by numerical studies for two-dimensional test problems
Subject Headings: advection problems
residual distribution
discrete maximum principles
matrix-free methods
Bernstein polynomials
high-order finite elements
Issue Date: 2019-12
Appears in Collections:Ergebnisberichte des Instituts für Angewandte Mathematik

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