Numerical methods for solving the cardiac electrophysiology model, which describes the electrical activity in the heart, are proposed. The model problem consists of a nonlinear reaction‐diffusion partial differential equation coupled to systems of ordinary differential equations that describes electrochemical reactions in cardiac cells. The proposed methods combine an operator splitting technique for the reaction‐diffusion equation with primal hybrid methods for spatial discretization considering continuous or discontinuous approximations for the Lagrange multiplier. A static condensation is adopted to form a reduced global system in terms of the multiplier only. Convergence studies exhibit optimal rates of convergence and numerical experiments show that the proposed schemes can be more efficient than standard numerical techniques commonly used in this context when preconditioned iterative methods are used for the solution of linear systems.

中文翻译：

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心脏单域方程的稳定混合不连续伽辽金有限元方法。

提出了用于求解描述心脏电活动的心脏电生理模型的数值方法。模型问题由非线性反应扩散偏微分方程组成，该方程与描述心肌细胞中电化学反应的常微分方程系统耦合。所提出的方法将反应扩散方程的算子分裂技术与考虑拉格朗日乘子的连续或不连续近似的空间离散化的原始混合方法相结合。仅就乘数而言，采用静态凝聚以形成简化的全局系统。