Journal of numerical mathematics: Improvements of algebraic flux-correction schemes based on Bernstein finite elements

Hajduk, Hennes

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Title:: Journal of numerical mathematics

Publication:: Berlin New York, NY: de Gruyter

Note:: Gesehen am 14.11.12

Scope:: Online-Ressource

ISSN:: 1569-3953

ZDB-ID:: 2095674-5

VÖBB-Katalog:: 15137074

Previous Title:: East west journal of numerical mathematics

Keywords:: Numerische Mathematik ; Zeitschrift

Classification:: Mathematik

Collection:: Mathematik

Copyright:: Rights reserved

Accessibility:: Eingeschränkter Zugang mit Nutzungsbeschränkungen

Article

Author:: Hajduk, Hennes

Title:: Improvements of algebraic flux-correction schemes based on Bernstein finite elements

Publication:: Berlin New York, NY: de Gruyter, 2025

Language:: English

Information:: Abstract: In Galerkin finite element schemes, the discrete first derivative operator for each spatial dimension is a square matrix that is skew-symmetric under restrictive assumptions for certain types of discretizations and boundary conditions. In most settings, however, this desirable property is violated, often only for a few pairs of nodes. These exceptions can invalidate certain design principles based on the skew-symmetry assumption made for these operators. This paper demonstrates that algebraic manipulations can be performed to make the discrete gradient operators of Bernstein polynomial-based finite element methods skew symmetric. Interest in such discretizations has recently been increasing because they represent natural extensions of second-order algebraic flux correction schemes to higher-order spaces. We employ the new operators in the context of such property-preserving methods, mostly based on discontinuous Galerkin discretizations of arbitrary order. Additional theoretical results for the schemes under investigation are derived, including local and global entropy inequalities, among others. Moreover, a discussion on the optimality of CFL-like time step restrictions arising in explicit Runge–Kutta methods shows that our new approach is superior to earlier representatives of operators employed in similar contexts. These techniques use the monolithic convex limiting paradigm and are applied to the compressible Euler equations.

Scope:: Online-Ressource

Note:: Open Access; Archivierung/Langzeitarchivierung gewährleistet

Keywords:: algebraic flux correction ; hyperbolic conservation laws ; skew-symmetric discrete gradients ; entropy stability ; Bernstein finite elements ; monolithic convex limiting ; 65M60

Classification:: Mathematik

URN:: urn:nbn:de:101:1-2511260237194.907919799942

Collection:: Mathematik

Copyright:: CC BY

Accessibility:: Free Access

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