2023/02/09 by Mieke Ten Eikelder, S. Stoter, Eikelder, M. ten +5
Decision Sciences · Engineering · #35L67 #65K10 #65N30 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.2302.04955
openalex publication_date 2023/02/09 · openalex created_date 2023/02/14 · openalex updated_date 2026/07/28
One of the major challenges in finite element methods is the mitigation of spurious oscillations near sharp layers and discontinuities known as the Gibbs phenomenon. In this article, we propose a set of functionals to identify spurious oscillations in best approximation problems in finite element spaces. Subsequently, we adopt these functionals in the formulation of constraints in an effort to eliminate the Gibbs phenomenon. By enforcing these constraints in best approximation problems, we can entirely eliminate over- and undershoot in one dimensional continuous approximations, and significantly suppress them in one- and higher-dimensional discontinuous approximations.