A 98%-effective lot-sizing rule for a multi-product, multi-stage production/inventory system
Mathematics of Operations Research
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle
Mathematics of Computation
Numerical Data Fitting in Dynamical Systems: A Practical Introduction with Applications and Software
Numerical Data Fitting in Dynamical Systems: A Practical Introduction with Applications and Software
SIAM Journal on Numerical Analysis
On the design of general-purpose flux limiters for finite element schemes. I. Scalar convection
Journal of Computational Physics
Journal of Computational Physics
Monotone finite volume schemes for diffusion equations on polygonal meshes
Journal of Computational Physics
Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes
Journal of Computational Physics
Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
A monotone finite volume method for advection-diffusion equations on unstructured polygonal meshes
Journal of Computational Physics
A segmentation-based algorithm for large-scale partially ordered monotonic regression
Computational Statistics & Data Analysis
Hi-index | 31.45 |
We suggest here a least-change correction to available finite element (FE) solution. This postprocessing procedure is aimed at recovering the monotonicity and some other important properties that may not be exhibited by the FE solution. Although our approach is presented for FEs, it admits natural extension to other numerical schemes, such as finite differences and finite volumes. For the postprocessing, a priori information about the monotonicity is assumed to be available, either for the whole domain or for a subdomain where the lost monotonicity is to be recovered. The obvious requirement is that such information is to be obtained without involving the exact solution, e.g. from expected symmetries of this solution. The postprocessing is based on solving a monotonic regression problem with some extra constraints. One of them is a linear equality-type constraint that models the conservativity requirement. The other ones are box-type constraints, and they originate from the discrete maximum principle. The resulting postprocessing problem is a large scale quadratic optimization problem. It is proved that the postprocessed FE solution preserves the accuracy of the discrete FE approximation. We introduce an algorithm for solving the postprocessing problem. It can be viewed as a dual ascent method based on the Lagrangian relaxation of the equality constraint. We justify theoretically its correctness. Its efficiency is demonstrated by the presented results of numerical experiments.