Abstract A generalized thermistor model is discretized thanks to a fully implicit vertex-centered finite volume scheme on simplicial meshes. An assumption on the stiffness coefficients is mandatory to prove a discrete maximum principle on the electric potential. This property is fundamental to handle the stability issues related to the Joule heating term. Then the convergence to a weak solution is established. Finally, numerical results are presented to show the efficiency of the methodology and to illustrate the behavior of the temperature together with the electric potential within the medium.

中文翻译：

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广义热敏电阻模型稳定有限体积方案的数值分析

摘要 由于单纯网格上的完全隐式以顶点为中心的有限体积方案，广义热敏电阻模型被离散化。为了证明电势的离散最大值原理，必须对刚度系数进行假设。此属性是处理与焦耳热项相关的稳定性问题的基础。然后建立对弱解的收敛。最后，给出了数值结果以显示该方法的效率并说明温度与介质内电势的行为。