We consider the monodomain model, a system of a parabolic semilinear reaction–diffusion equation coupled with a nonlinear ordinary differential equation, arising from the (simplified) mathematical description of the electrical activity of the heart. We derive a posteriori error estimators accounting for different sources of error (space/time discretization and linearization). We prove reliability and efficiency (this latter under a suitable assumption) of the error indicators. Finally, numerical experiments assess the validity of the theoretical results.

中文翻译：

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心脏电生理中单域模型的后验误差估计

我们考虑单域模型，它是由抛物线形半线性反应扩散方程与非线性常微分方程耦合而成的系统，是由心脏电活动的（简化）数学描述产生的。我们得出了后验误差估计量，说明了误差的不同来源（空间/时间离散化和线性化）。我们证明了误差指标的可靠性和效率（在适当的假设下，后者是有效的）。最后，数值实验评估了理论结果的有效性。