Analysis of algebraic flux correction schemes for semi-discrete advection problems
| dc.contributor.author | Hajduk, Hennes | |
| dc.contributor.author | Rupp, Andreas | |
| dc.date.accessioned | 2025-04-14T06:18:55Z | |
| dc.date.available | 2025-04-14T06:18:55Z | |
| dc.date.issued | 2023-01-30 | |
| dc.description.abstract | Based on recent developments regarding the analysis of algebraic flux correction schemes, we consider a locally bound-preserving discretization of the time-dependent advection equation. Specifically, we analyze a monolithic convex limiting scheme based on piecewise (multi-)linear continuous finite elements in the semi-discrete formulation. To stabilize the discretization, we use low order time derivatives in the definition of raw antidiffusive fluxes. Our analytical investigation reveals that their limited counterparts should satisfy a certain compatibility condition. The conducted numerical experiments suggest that this prerequisite is satisfied unless the size of mesh elements is vastly different.We prove global-in-time existence of semi-discrete approximations and derive an a priori error estimate for finite time intervals with a worst-case convergence rate of 1 2 w. r. t. the L2 error. This rate is optimal in the setting under consideration because we allow all correction factors of the flux-corrected scheme to become zero. In this case, the algorithm reduces to the bound-preserving discrete upwinding method but the limited counterpart of this scheme converges much faster, in practice. Additional numerical experiments are performed to verify the provable convergence rate for a few variants of the scheme. | en |
| dc.identifier.uri | http://hdl.handle.net/2003/43662 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-25435 | |
| dc.language.iso | en | |
| dc.relation.ispartofseries | BIT : numerical mathematics; 63(1) | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Algebraic flux correction | en |
| dc.subject | Time-dependent advection equation | en |
| dc.subject | Stability and a priori error estimates | en |
| dc.subject | Monolithic limiting | en |
| dc.subject | Semi-discrete analysis | en |
| dc.subject.ddc | 510 | |
| dc.title | Analysis of algebraic flux correction schemes for semi-discrete advection problems | en |
| dc.type | Text | |
| dc.type.publicationtype | Article | |
| dcterms.accessRights | open access | |
| eldorado.secondarypublication | true | |
| eldorado.secondarypublication.primarycitation | Hajduk, H. and Rupp, A. (2023) ‘Analysis of algebraic flux correction schemes for semi-discrete advection problems’, BIT : numerical mathematics, 63(1), p. 8. Available at: https://doi.org/10.1007/s10543-023-00957-z | |
| eldorado.secondarypublication.primaryidentifier | https://doi.org/10.1007/s10543-023-00957-z |