REVIEW 1 cited by
A nodally bound-preserving finite element method for hyperbolic convection-reaction problems
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
In this article, we present a numerical approach to ensure the preservation of physical bounds on the solutions to linear and nonlinear hyperbolic convection-reaction problems at the discrete level. We provide a rigorous framework for error analysis, formulating the discrete problem as a variational inequality and demonstrate optimal convergence rates in a natural norm. We summarise extensive numerical experiments validating the effectiveness of the proposed methods in preserving physical bounds and preventing unphysical oscillations, even in challenging scenarios involving highly nonlinear reaction terms.
Forward citations
Cited by 1 Pith paper
-
A Positivity-Preserving Finite Element Framework for Accurate Dose Computation in Proton Therapy
A positivity-preserving SUPG/variational-inequality finite element scheme is introduced for proton transport dose computation, with claimed error estimates and benchmark tests.
Discussion (0). Continue with ORCID to comment.