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Teaching at Uni Hamburg (summer 2018)
Numerical Approximation of PDEs by Finite Differences and Finite Volumes (lecture and exercises)
- see STiNE for resources and exercises

Office hours at Uni Hamburg
Mo., 10:00 - 11:00, and by appointment

Theoretical and numerical treatment of evolutionary PDEs, in particular hyperbolic conservation laws. Numerical analysis of high order finite volume and discontinuous Galerkin methods, generalized Riemann problems, WENO schemes, entropy stability

Claus R. Goetz, Dinshaw S. Balsara, Michael Dumbser: A family of HLL-type solvers for the generalized Riemann problem,
to appear in Computers and Fluids

Claus R. Goetz, Michael Dumbser: A square entropy stable flux limiter for PNPM schemes,
preprint (2016)

Claus R. Goetz, Michael Dumbser: A novel solver for the generalized Riemann problem based on a simplified LeFloch-Raviart expansion and a local space-time discontinuous Galerkin formulation,
J. Sci. Comput. 69 (2016), pp. 805 - 840

Claus R. Goetz, Armin Iske: Approximate solutions of generalized Riemann problems for nonlinear systems of hyperbolic conservation laws,
Math. Comp. 85, No 297 (2016), pp. 35-62 (preprint)

Claus R. Goetz, Armin Iske: Approximate solutions of generalized Riemann problems: The Toro-Titarev solver and the LeFloch-Raviart expansion ,
Numerical Methods for Hyperbolic Equations: Theory and Applications, M. E. Vásques-Cedón and A. Hidalgo and P. García-Navarro and L. Cea, eds., Taylor-Francis Group, 2013, pp. 267 - 275

Dissertation:
Approximate Solutions of Generalized Riemann Problems for Hyperbolic Conservation Laws and Their Application to High Order Finite Volume Schemes ,
Universität Hamburg, 2013 (full text at Staats- und Universitätsbibliothek Hamburg)

Upcoming

International Conference on Spectral and High Order Methods (ICOSAHOM 2018), July 9-13, 2018, London (UK),

XVII International Conference on Hyperbolic Problems Theory, Numerics, Applications (HYP 2018) June 25-29, 2018, University Park, PN (USA)

Past (selected)

European Conference on High Order Nonlinear Numerical Methods for Evolutionary PDEs: Theory and Applications (HONOM 2017), March 27-31, 2017, Stuttgart (Germany),
Talk: A square entropy stable flux limiter for PNPM schemes

Recent trends and future developments in Computational Science and Engineering, Workshop of the Lothar Collatz Center (LCS-CSE), March 22 -24, 2017, Plön (Germany),
Talk: A family of HLL-type solvers for the generalized Riemann problem

Fifth Chilean Workshop on Numerical Analysis of Partial Differential Equations ( WONAPDE2016 ), January 11-15, 2016, Concepción (Chile),
Talk: An ADER scheme with a new solver for the generalized Riemann problem and local space-time DG flux integration

European Conference on High Order Nonlinear Numerical Methods for Evolutionary PDEs: Theory and Applications (HONOM 2015), March 16-20, 2015, Trento (Italy),
Talk: A novel GRP solver for the ADER method based on a simplified LeFloch-Ravaiart expansion

Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs, A Conference in Honor of Eitan Tadmor's 60th Birthday (TN60), April 28 - May 2, 2014, Bethesda, MD (USA)

European Conference on High Order Nonlinear Numerical Methods for Evolutionary PDEs: Theory and Applications (HONOM 2013), March, 18-22, 2013, Bordeaux (France),
Talk: Approximate solutions of generalized Riemann problems for nonlinear systems of hyperbolic conservation laws.

Numerical Methods for Hyperbolic Equations: Theory and Applications, International Conference to honour Professor E.F. Toro in the month of his 65th birthday (NMHETATORO65), July 4-8, Santiago de Compostela (Spain),
Talk: The Toro-Titarev solver and the LeFloch-Raviart expansion for the generalized Riemann problem.

European Conference on High Order Nonlinear Numerical Methods for Evolutionary PDEs: Theory and Applications (HONOM 2011), April 11-15, 2011, Trento (Italy),
Talk: On the Analysis of a Solver for Genaralized Riemann Problems by Asymptotic Expansion.