Numerische Mathematik

, Volume 135, Issue 2, pp 547–569 | Cite as

Error analysis of implicit Euler methods for quasilinear hyperbolic evolution equations

  • Marlis HochbruckEmail author
  • Tomislav Pažur


In this paper we study the convergence of the semi-implicit and the implicit Euler methods for the time integration of abstract, quasilinear hyperbolic evolution equations. The analytical framework considered here includes certain quasilinear Maxwell’s and wave equations as special cases. Our analysis shows that the Euler approximations are well-posed and convergent of order one. The techniques will be the basis for the future investigation of higher order time integration methods and full discretizations of certain quasilinear hyperbolic problems.

Mathematics Subject Classification

Primary 65M12 65J15 Secondary 35Q61 35L90 



The authors thank Roland Schnaubelt and Dominik Müller for helpful discussions on the well-posedness of the Euler approximations. We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) through RTG 1294 and CRC 1173.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute for Applied and Numerical MathematicsKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.AVL AST d.o.o. Croatia10020Croatia

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