WIAS Preprint No. 2378, (2017)

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



Authors

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

2010 Mathematics Subject Classification

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

Keywords

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

DOI

10.20347/WIAS.PREPRINT.2378

Abstract

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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