High-order bounds-satisfying approximation of partial differential equations via finite element variational inequalities

• Published in: Numerische Mathematik Vol. 156; no. 3; pp. 927 - 947
• Main Authors: Kirby, Robert C., Shapero, Daniel
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2024; Springer Nature B.V
• Subjects: Accuracy; Approximation; Constraints; Finite difference method; Finite element method; Inequalities; Mathematical analysis; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Numerical Analysis; Numerical and Computational Physics; Partial differential equations; Polynomials; Simulation; Theoretical; 65N12; 65N30; 41A29

Solutions to many important partial differential equations satisfy bounds constraints, but approximations computed by finite element or finite difference methods typically fail to respect the same conditions. Chang and Nakshatrala (Comput Methods Appl Mech Eng 320:287–334, 2017) enforce such bounds...