This paper presents a new approach to constraining the eigenvalue range of symmetric tensors in numerical advectionschemes based on the flux-corrected transport (FCT) algorithm and a continuous finite element discretization. In thecontext of element-based FEM-FCT schemes for scalar conservation laws, the numerical solution is evolved usinglocal extremum diminishing (LED) antidi usive corrections of a low order approximation which is assumed to satisfythe relevant inequality constraints. The application of a limiter to antidi usive element contributions guarantees thatthe corrected solution remains bounded by the local maxima and minima of the low order predictor.The FCT algorithm to be presented in this paper guarantees the LED property for the largest and smallest eigenvaluesof the transported tensor at the low order evolution step. At the antidi usive correction step, this property ispreserved by limiting the antidi usive element contributions to all components of the tensor in a synchronized manner.The definition of the element-based correction factors for FCT is based on perturbation bounds for auxiliarytensors which are constrained to be positive semidefinite to enforce the generalized LED condition. The derivation ofsharp bounds involves calculating the roots of polynomials of degree up to 3. As inexpensive and numerically stablealternatives, limiting techniques based on appropriate approximations are considered. The ability of the new limitersto enforce local bounds for the eigenvalue range is confirmed by numerical results for 2D advection problems.
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