Christoph Erath

Offizielle akademische Titel: (HProf. Priv.-Doz. Dipl.-Ing. Dr.rer.nat.)


PH Vorarlberg

(University College of Teacher Education Vorarlberg)

Liechtensteinerstraße 33-37
6800 Feldkirch, Austria

‭Raum:   128
Tel.:       +43 (0)5522 31199-122
E-Mail:  christoph.erath(at)ph-vorarlberg.ac.at

Visitenkarte

HPce

I am a Professor in Mathematics. I study different aspects of numerical schemes for partial differential equations.

Some research interests:

  • Schemes: Finite Element Methods (FEM), Finite Volume Methods (FVM), Boundary Element Methods (BEM), Discontinuous Galerkin Methods (DGM), Coupling
  • A priori and a posteriori error (robust) analysis 
  • Adaptivity, mesh refinement strategies 
  • Numerical schemes for climate modeling 
  • Developing of new teaching formats in cooperation with local companies

The relation of my research area to a topic for a school lecture
is reflected in the slides (in German)

Mathematik einmal ungenau, oder doch nicht?
Können wir unsere Welt im Schlunterricht approximieren?

 

Refeered Publications (at least two referees)

2022 (27)

C. Erath, L. Mascotto, J. M. Melenk, I. Perugia, and A. Rieder.
Mortar Coupling of hp-Discontinuous Galerkin and Boundary Element Methods for the Helmholtz Equation,
J. Sci. Comput. 92(2): 1-41, 2022.
DOI: /10.1007/s10915-022-01849-0

2021 (26)M. Elasmi, C. Erath, and S. Kurz.
Non-symmetric isogeometric FEM-BEM couplings,
Adv. Comput. Math. 47(61): 1-36, 2021.
DOI: /10.1007/s10444-021-09886-3 (Open Access)
2020 (25)C. Erath and R. Schorr.
Stable Non-symmetric Coupling of the Finite Volume Method and the Boundary Element Method for Convection-Dominated Parabolic-Elliptic Interface Problems, 
Comput. Methods Appl. Math. 20(2): 251-272, 2020.
DOI: 10.1515/cmam-2018-0253
2020 (24)C. Erath, G. Gantner, and D. Praetorius.
Optimal convergence behavior of adaptive FEM driven by simple (h-h/2)-type error estimators, 
Comput. Math. Appl. 79(3): 623-642, 2020.
DOI: 10.1016/j.camwa.2019.07.014
2019 (23)C. Erath and D. Praetorius.
Optimal adaptivity for the SUPG finite element method, 
Comput. Methods Appl. Mech. Engrg. 353: 308-327, 2019.
DOI: 10.1016/j.cma.2019.05.028
2019 (22)C. Erath and D. Praetorius.
Adaptive vertex-centered finite volume methods for general second-order linear elliptic partial differential equations, 
IMA J. Numer. Anal. 39(2): 983-1008, 2019.
DOI: 10.1093/imanum/dry006
2019 (21)C. Erath and R. Schorr. 
A simple boundary approximation for the non-symmetric coupling of the finite element method and the boundary element method for parabolic-elliptic interface problems, 
Numerical Mathematics and Advanced Applications. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, Springer, Volume 126, 993-1001, 2019.
DOI: 10.1007/978-3-319-96415-7_94
2018 (20)H. Egger, C. Erath, and R. Schorr.
On the nonsymmetric coupling method for parabolic-elliptic interface problems, 
SIAM J. Numer. Anal. 56(6): 3510-3533, 2018.
DOI: 10.1137/17M1158276
2017 (19)C. Erath and R. Schorr. 
Comparison of adaptive non-symmetric and three-field FVM-BEM coupling, 
Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems, Springer Proceedings in Mathematics & Statistics, Volume 200, 337-345, 2017.
DOI: 10.1007/978-3-319-57394-6_36
2017 (18)C. Erath and D. Praetorius. 
Céa-type quasi-optimality and convergence rates for (adaptive) vertex-centered FVM, 
Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects, Springer Proceedings in Mathematics & Statistics, Volume 199, 215-223, 2017.
DOI: 10.1007/978-3-319-57397-7_14
2017 (17)C. Erath and R. Schorr. 
An adaptive non-symmetric finite volume and boundary element coupling method for a fluid mechanics interface problem, 
SIAM J. Sci. Comput. 39(3): A741-A760, 2017.
DOI: 10.1137/16M1076721
2017 (16)C. Erath, G. Of, and F.-J. Sayas. 
A non-symmetric coupling of the finite volume method and the boundary element method, 
Numer. Math. 135(3): 895-922, 2017.
DOI: 10.1007/s00211-016-0820-3
2016 (15)C. Erath and D. Praetorius.
Adaptive vertex-centered finite volume methods with convergence rates,  
SIAM J. Numer. Anal. 54(4): 2228-2255, 2016.
DOI: 10.1137/15M1036701
2016 (14)C. Erath, M. A. Taylor, and R. D. Nair.
Two conservative multi-tracer efficient semi-Lagrangian schemes for multiple processor systems integrated in a spectral element (climate) dynamical core,
Commun. Appl. and Ind. Math., special issue on New trends in semi-Lagrangian methods, 7(3): 71-95, 2016.
DOI: 10.1515/caim-2016-0023 (Open Access)
2015 (13)C. Erath.
A nonconforming a posteriori estimator for the coupling of cell-centered finite volume and boundary element methods, 
Numer. Math. 131(3): 425-451, 2015.
DOI: 10.1007/s00211-014-0694-1
2014 (12)C. Erath.
Comparison of two Couplings of the Finite Volume Method and the Boundary Element Method, 
Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects, Springer Proceedings in Mathematics & Statistics, Volume 77, 255-263, 2014.
DOI: 10.1007/978-3-319-05684-5_24
2014 (11)C. Erath and R. D. Nair.
A conservative multi-tracer transport scheme for spectral-element spherical grids, 
J. Comput. Phys. 256: 118-134, 2014.
DOI: 10.1016/j.jcp.2013.08.050
2013 (10)C. Erath.
A posteriori error estimates and adaptive mesh refinement for the coupling of the finite volume method and the boundary element method, 
SIAM J. Numer. Anal. 51(3): 1777-1804, 2013. 
DOI: 10.1137/110854771
2013 (9)C. Erath.
A new conservative numerical scheme for flow problems on unstructured grids and unbounded domains, 
J. Comput. Phys. 245: 476-492, 2013.
DOI: 10.1016/j.jcp.2013.03.055
2013 (8)C. Erath, P. H. Lauritzen, and H. M. Tufo.
On mass-conservation in high-order high-resolution rigorous remapping schemes on the sphere, 
Mon. Weather Rev. 141(6): 2128-2133, 2013.
DOI: 10.1175/MWR-D-13-00002.1 (Open Access)
2012 (7)C. Erath, S. A. Funken, P. Goldenits, and D. Praetorius.
Simple error estimations for Galerkin BEM for some hypersingular integral equation in 2D, 
Appl. Anal. 92(6): 1194-1216, 2013.
DOI: 10.1080/00036811.2012.661045
2012 (6)C. Erath, P. H. Lauritzen, J. H. Garcia, H. M. Tufo.
Integrating a scalable and efficient semi-Lagrangian multi-tracer transport scheme in HOMME, 
Procedia Computer Science (ERA A-ranked) 9: 994-1003, 2012. 
DOI: 10.1016/j.procs.2012.04.106 (Open Access)
2012 (5)C. Erath.
Coupling of the finite volume element method and the boundary element method: an a priori convergence result,
SIAM J. Numer. Anal. 50(2): 574-594, 2012. 
DOI: 10.1137/110833944
2011 (4)P. H. Lauritzen, C. Erath, and R. Mittal.
On simplifying 'incremental remap'-based transport schemes, 
J. Comput. Phys., 230(22): 7957-7963, 2011. 
DOI: 10.1016/j.jcp.2011.06.030
2009 (3)C. Erath, S. Ferraz-Leite, S. A. Funken, and D. Praetorius.
Energy norm based a posteriori error estimation for boundary element methods in two dimensions, 
Appl. Numer. Math., 59(11): 2713-2734, 2009. 
DOI: 10.1016/j.apnum.2008.12.024
2008 (2)C. Erath, S. A. Funken, and D. Praetorius.
Adaptive Cell-Centered Finite Volume Method,
Finite Volumes for Complex Applications V, Wiley (ISBN: 978-1-84821-035-6) , 359-366, 2008.
2008 (1)C. Erath and D. Praetorius. 
A posteriori error estimate and adaptive mesh refinement for the cell-centered finite volume method for elliptic boundary value problems, 
SIAM J. Numer. Anal., 47(1): 109-135, 2008.
DOI: 10.1137/070702126

Proceedings (publications for marketing)

2016C. Erath, G. Of, and F.-J. Sayas.
A non symmetric FVM-BEM coupling method,
PAMM, 16(1): 743-744, 2016. 18th annual meeting GAMM.
DOI: 10.1002/pamm.201610360 (Open Access)

 

Betreuung von Bachelor- und Masterarbeiten in verschiedenen mathematischen Themengebieten.

Regelmässige Lehrveranstaltungen:

Wintersemester

  • VO Angewandte Mathematik (3 SSt)
  • PS Angewandte Mathematik (3 SSt)

Sommersemester

  • VO Analysis 2 für Lehramtsstudierende (4 SSt)
  • PS Analysis 2 für Lehramtsstudierende (3 SSt)
  • VO Partielle Differentialgleichungen für Lehramtsstudierende(2 SSt)
  • SE Seminar mit Bachelorarbeit(2 SSt)
  • PJ Masterarbeit
2021 (28)M. Elasmi, C. Erath, and S. Kurz.
The Johnson-Nédélec FEM-BEM Coupling for magnetostatic problems in the isogeometric framework.
Available on arXiv:2110.04150.

 

 

Short CV

  • since September 2020: Professor at the University College of Teacher Education Vorarlberg (PH Vorarlberg, Austria)
  • In December 2020 (finalization Oktober 2020) I was awarded the venia docendi (Habilitation, Privatdozent) from TU Wien (Austria) in Applied Mathematics.
  • From September 2014 to August 2020 I was a Professor for Numerical Mathematics at TU Darmstadt (Germany) at Department of Mathematics (Numerical Analysis and Scientific Computing group). I was the head of a team (PostDoc and PhD). My performance was positiv evaluated in June 2017 (equivalent to a habilitation).
  • Assistant (Univ. Ass. with teaching) from September 2013 to August 2014 at the Faculty of Mathematics, University of Vienna, Austria.
  • PostDoc from August 2010 to July 2013 at National Center for Atmospheric Research and University of Colorado at Boulder in Boulder, Colorado, USA.
  • PhD (Dr. rer. nat., summa cum laude, July 2010) in Mathematics from Ulm University, Germany.
  • University Assistant (with teaching) from October 2005 to August 2010 at the Institute for Numerical Mathematics, University of Ulm, Germany.
  • Master degree (Dipl.-Ing., with honor, October 2005) in Technical Mathematics from the TU Wien, Austria.
     

Selected Grants and Awards

My research was honored by several grants and awards. , e.g.:

  • Award 2012 from the Ulmer Universitätsgesellschaft for my PhD Thesis
  • PhD scholarship from the federal state Baden-Württemberg, Germany, March 2007 - February 2010
  • Award 2006 from the Austrian Mathematical Society (ÖMG) for my Diploma Theses