WIAS Preprint No. 2378, (2017)

Hybrid finite-volume/finite-element schemes for $p(x)$-Laplace thermistor models


  • Fuhrmann, Jürgen
    ORCID: 0000-0003-4432-2434
  • Glitzky, Annegret
    ORCID: 0000-0003-1995-5491
  • Liero, Matthias
    ORCID: 0000-0002-0963-2915

2010 Mathematics Subject Classification

  • 65M08 35J92 35G60 35Q79 80M12 80A20


  • Finite volume scheme, p(x)-Laplace thermistor model, path following




We introduce an empirical PDE model for the electrothermal description of organic semiconductor devices by means of current and heat flow. The current flow equation is of p(x)-Laplace type, where the piecewise constant exponent p(x) takes the non-Ohmic behavior of the organic layers into account. Moreover, the electrical conductivity contains an Arrhenius-type temperature law. We present a hybrid finite-volume/finite-element discretization scheme for the coupled system, discuss a favorite discretization of the p(x)-Laplacian at hetero interfaces, and explain how path following methods are applied to simulate S-shaped current-voltage relations resulting from the interplay of self-heating and heat flow.

Appeared in

  • Finite Volumes for Complex Applications VIII -- Hyperbolic, Elliptic and Parabolic Problems -- FVCA 8, Lille, France, June 2017, C. Cancès, P. Omnes, eds., Springer International Publishing, Cham et al., 2017, pp. 397--405.

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