Download or read book Physics-Compatible Finite Element Methods for Scalar and Tensorial Advection Problems written by Christoph Lohmann and published by Springer Nature. This book was released on 2019-10-14 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Christoph Lohmann introduces a very general framework for the analysis and design of bound-preserving finite element methods. The results of his in-depth theoretical investigations lead to promising new extensions and modifications of existing algebraic flux correction schemes. The main focus is on new limiting techniques designed to control the range of solution values for advected scalar quantities or the eigenvalue range of symmetric tensors. The author performs a detailed case study for the Folgar-Tucker model of fiber orientation dynamics. Using eigenvalue range preserving limiters and admissible closure approximations, he develops a physics-compatible numerical algorithm for this model.