A Space-Time Adaptive Finite Element Method with Exponential Time Integrator for the Phase Field Model of Pitting Corrosion

Huadong Gao, Lili Ju, Xiao Li, Ravindra Duddu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

16 Citations (Scopus)


In this paper we propose a space-time adaptive finite element method for the phase field model of pitting corrosion, which is a parabolic partial differential equation system consisting of a phase variable and a concentration variable. A major challenge in solving this phase field model is that the problem is very stiff, which makes the time step size extremely small for standard temporal discretizations. Another difficulty is that a high spatial resolution is required to capture the steep gradients within the diffused interface, which results in very large number of degrees of freedom for uniform meshes. To overcome the stiffness of this model, we combine the Rosenbrock–Euler exponential integrator with Crank–Nicolson scheme for the temporal discretization. Moreover, by exploiting the fact that the speed of the corroding interface decreases with time, we derive an adaptive time stepping formula. For the spatial approximation, we propose a simple and efficient strategy to generate adaptive meshes that reduces the computational cost significantly. Thus, the proposed method utilizes local adaptivity and mesh refinement for efficient simulation of the corrosive dissolution over long times in heterogeneous media with complex microstructures. We also present an extensive set of numerical experiments in both two and three dimensional spaces to demonstrate efficiency and robustness of the proposed method.

Original languageEnglish
Article number109191
JournalJournal of Computational Physics
Publication statusPublished - 1 Apr 2020


  • Adaptivity
  • Exponential integrator
  • Finite element method
  • Phase field model
  • Pitting corrosion
  • Semi-implicit scheme

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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