Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. An error estimate in H¹ norm is obtained for a piecewise finite element approximation to the solution of the nonlinear steady-state Poisson-Nernst-Planck equations. Some superconvergence results are also derived by using the gradient recovery technique for the equations. Numerical results are given to validate the theoretical results. It is also numerically illustrated that the gradient recovery technique can be successfully applied to the computation of the practical ion channel problem to improve the efficiency of the external iteration and save CPU time.

Poisson-Nernst-Planck方程广泛用于描述溶剂化生物分子系统中离子的电扩散。对于非线性稳态Poisson-Nernst-Planck方程的解的分段有限元近似，获得了H ¹范数的误差估计。通过对方程使用梯度恢复技术，还可以得出一些超收敛结果。数值结果验证了理论结果。还从数值上说明了梯度恢复技术可以成功地应用于实际离子通道问题的计算，以提高外部迭代的效率并节省CPU时间。