Efficient Dynamically Regularized Lagrange Multiplier Schemes with Energy Dissipation for Pitting Corrosion

In this paper, a series of efficient decoupled dynamically regularized Lagrange multiplier schemes with guaranteed energy dissipation are developed for phase-field modeling of pitting corrosion coupled with ionic concentration, and their energy-dissipation properties are rigorously analyzed. The proposed method requires only the solution of a few constant-coefficient elliptic equations and a single nonlinear algebraic equation per time step, resulting in a significantly reduced computational cost for the coupled system. The resulting system preserves the discrete energy decay unconditionally at each time step. An adaptive space-time finite element algorithm is employed to efficiently resolve the evolving corrosion front and steep concentration gradients. Combined with a decoupled iterative solver and a mass-lumped finite element method, the scheme achieves high computational efficiency and robustness. Numerical results confirm that the scheme not only reliably captures pit nucleation and evolution with substantially reduced computational cost but also exhibits strong overall applicability to real-world challenges.