Physics-Compatible Finite Element Methods for Scalar and Tensorial Advection Problems

  • Christoph Lohmann

Table of contents

  1. Front Matter
    Pages I-XII
  2. Christoph Lohmann
    Pages 1-13
  3. Christoph Lohmann
    Pages 15-34
  4. Christoph Lohmann
    Pages 35-52
  5. Christoph Lohmann
    Pages 53-149
  6. Christoph Lohmann
    Pages 151-210
  7. Christoph Lohmann
    Pages 211-261
  8. Christoph Lohmann
    Pages 263-269
  9. Back Matter
    Pages 271-283

About this book


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.


  • Equations of Fluid Dynamics
  • Finite Element Discretization
  • Limiting for Scalars
  • Limiting for Tensors
  • Simulation of Fiber Suspensions

Target Groups

  • Researchers and students in the field of applied mathematics
  • Developers of numerical methods for transport equations and of general-purpose simulation software for computational fluid dynamics, engineers in the field of fiber suspension flows and injection molding processes

The Author

Christoph Lohmann is a postdoctoral researcher in the Department of Mathematics at TU Dortmund University. His research activities are focused on numerical analysis of finite element methods satisfying discrete maximum principles.


High-Resolution Schemes Discrete Maximum Principles Flux-Corrected Transport Algebraic Flux Correction Eigenvalue Range Limiting Folgar-Tucker Equation Advection Problems

Authors and affiliations

  • Christoph Lohmann
    • 1
  1. 1.DortmundGermany

Bibliographic information

  • DOI
  • Copyright Information Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2019
  • Publisher Name Springer Spektrum, Wiesbaden
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-658-27736-9
  • Online ISBN 978-3-658-27737-6
  • Buy this book on publisher's site