PH-Online

Infos für...

Moodle

Bibliothek

Suche

.

Skip to main content

Christoph Erath


PH 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

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 
  • Scientific Computing: efficient numerical realization of transport schemes for atmospheric modeling and their coupling to spectral elements (HOMME-SE) on multi-core platforms for the new dynamical core of CAM (Community Atmosphere Model).

 

  Refeered Publications (at least two referees)

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
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
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
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)

10/2016C. 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

 

2020 (26)M. Elasmi, C. Erath, and S. Kurz.
Non-symmetric isogeometric FEM-BEM couplings.
Available on arXiv:2007.09057.

 

  • In December 2020 (finalization Oktober 2020) I was awarded the venia docendi (Habilitation, Privatdozent) from TU Wien (Austria) in Applied Mathematics.
  • PhD (Dr. rer. nat., summa cum laude, July 2010) in Mathematics from Ulm University (Ulm, Germany)
  • Master degree (Dipl.-Ing., with honor, October 2005) in Mathematics in Computer Science from the TU Wien (Vienna, Austria).

 

10/2020

Habilitation Thesis
Advanced Numerical Methods for Fluid Mechanics Problems - Theory, Analysis, Numerics, and Application,
TU Wien, Austria, 2020.
04/2010PhD Thesis
Coupling of the Finite Volume Method and the Boundary Element Method - Theory, Analysis, and Numerics,
Ulm University, Germany, 2010.
DOI: 10.18725/OPARU-1794
09/2005Diploma Thesis (in German)
Adaptive Finite Volumen Methode, Diploma Thesis in German,
TU Wien, Austria, 2005.

Nach oben