A Finite Element Method For A Class Of Cardiac Electrophysiological Mathematical Models

In the past few decades,as one of the important tools of scientific calculation,finite element method has achieved unprecedented development and is widely used in various fields such as physics,chemistry,medicine and so on.This paper is concerned with finite element computation of a semilinear elliptic equation with discontinuous coefficients arising from cardiac electrophysiology.We employ the usual conforming linear element to approximate the resulting nonlinear variational problem and prove the convergence of the finite element solutions as the mesh size tends to zero.Furthermore,a reliable and efficient residual-based a posteriori error estimator is derived to measure the discretization error in the H~1-norm.Finally,numerical results are provided to verify the theoretical findings.