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Numerische Mathematik

, Volume 143, Issue 4, pp 749–780 | Cite as

Numerical analysis of quasilinear parabolic equations under low regularity assumptions

  • Eduardo Casas
  • Konstantinos ChrysafinosEmail author
Article
  • 131 Downloads

Abstract

In this paper, we carry out the numerical analysis of a class of quasilinear parabolic equations, where the diffusion coefficient depends on the solution of the partial differential equation. The goal is to prove error estimates for the fully discrete equation using discontinuous Galerkin discretization in time DG(0) combined with piecewise linear finite elements in space. This analysis is performed under minimal regularity assumptions on the data. In particular, we omit any assumption regarding existence of a second derivative in time of the solution.

Mathematics Subject Classification

Primary 35K59 65M60 Secondary 35B65 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de TelecomunicaciónUniversidad de CantabriaSantanderSpain
  2. 2.Department of Mathematics, School of Applied Mathematics and Physical SciencesNational Technical University of AthensAthensGreece
  3. 3.IACMFORTHHeraklionGreece

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