A family of two-grid partially penalized immersed finite element methods for semi-linear parabolic interface problems (Q2051106)

The authors propose a family of two-grid algorithms for semi-linear parabolic interface problems based on partially penalized immersed finite element discretizations. Under the standard piecewise \(H^2\) regularity assumption for the exact solution, optimal \textit{a priori} error estimates are derived both in the energy norm and in the \(L^2\) norm. For nonlinear inputs, the two-grid methods are investigated based on Newton method. The efficiency of the proposed methods is theoretically and numerically illustrated.