Research Interests

Numerical analysis of discretization methods for partial differential equations; in particular:

• Finite Volume/Finite Element Methods
• Discretization of parameter-sensitive problems
• Evolution equations
• A posteriori error estimates and adaptivity
• Mesh generation and refinement

Recent Publications

Recent papers:

• Lutz Angermann, Peter Knabner, Andreas Rupp: Error estimates for completely discrete FEM in energy-type and weaker norms. Numerical Methods for Partial Differential Equations, 40(6):e23106, 2024.
• Finite element solution of a radiation/propagation problem for a Helmholtz equation with a compactly supported nonlinearity. Far East J. of Applied Mathematics, 116(4):311-356, 2023.
• Asad Anees, Lutz Angermann: An energy stable discontinuous Galerkin time-domain finite element method in optics and photonics. Results in Applied Mathematics, 19, 100393, 2023.
• A radiation and propagation problem for a Helmholtz equation with a compactly supported nonlinearity. Comm. Nonlinear Sci. Numer. Simul.126, 107422, 2023.
• Energy-Stability of Time-Domain Finite Element Solutions to Maxwell's Equations with Cubic Polarization. Proceedings of the 2022 IEEE 2nd Ukrainian Microwave Week (UkrMW), Kharkiv, Ukraine, November 14-18, 2022, 444-448.
• Asad Anees, Lutz Angermann: Energy stable time domain finite element methods for nonlinear models in Optics and Photonics. Internat. J. Numer. Anal. Mod., 19(4):511-541, 2022.
• Lutz Angermann: Formulation and investigation of a mathematical model for resonance radiation on media with compactly supported nonlinearities. Proceedings of the2021 IEEE XXVIth International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED),Tblisi, Georgia, September 8 - 10, 2021, 3-6 (plenary paper).

Books edited:

• Numerical Simulations - Applications, Examples and Theory. InTech, 2011, ISBN: 978-953-307-440-5, 520 p.
• Numerical Simulations - Examples and Applications in Computational Fluid Dynamics. InTech, 2010, ISBN: 978-953-307-153-4, 440 p.

Books:

• Lutz Angermann, Bernd Mulansky: Basic Course in Analysis and Linear Algebra. Springer Spektrum, Berlin-Heidelberg 2022, Softcover ISBN: 978-3-662-65595-5, eBook ISBN: 978-3-662-65596-2. 2nd edition of the 2018 work.
• Peter Knabner, Lutz Angermann:Numerical Methods for Elliptic and Parabolic Partial Differential Equations. Texts in Applied Mathematics, Vol. 44, 2nd revised and extended ed., Springer Nature, Cham 2021, Hardcover ISBN: 978-3-030-79384-5, eBook ISBN: 978-3-030-79385-2, Errata.
• Lutz Angermann, Vasyl V. Yatsyk:Resonant Scattering and Generation of Waves. Cubically Polarizable Layers.Springer, Cham 2019, ISBN: 978-3-319-96300-6 (print), 978-3-319-96301-3 (online), Errata.
• Lutz Angermann, Bernd Mulansky:Analysis and Linear Algebra I&II. edition winterwork, Leipzig 2018, ISBN: 978-3-96014-514-1 (print), 978-3-96014-522-6 (e-book).
• Peter Knabner, Lutz Angermann: Numerical Methods for Elliptic and Parabolic Partial Differential Equations. Texts in Applied Mathematics, Vol. 44, Springer-Verlag, New York 2003, ISBN: 0-387-95449-X.
• Peter Knabner, Lutz Angermann:Numerics of Partial Differential Equations. An application-oriented introduction. Springer textbook. Springer-Verlag, Berlin 2000, ISBN: 3-540-66231-6.

Complete list of publications:[pdf]

Erdös Number: 3

Mathematics Genealogy Project: Dept. of Mathematics, NDSU

Editorial Board member

of the Open Access journalRMS: Research in Mathematics & Statistics(Taylor & Francis Group), formerly known as Cogent Mathematics & Statistics, 2014-2022