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math.NA2025
Geometric local parameterization for solving Hele-Shaw problems with surface tension
Zengyan Zhang, Wenrui Hao, John Harlim
In this work, we introduce a novel computational framework for solving the two-dimensional Hele-Shaw free boundary problem with surface tension. The moving boundary is represented…
math.NA2025
Optimal error estimates of the diffuse domain method for parabolic equations
Wenrui Hao, Lili Ju, Yuejin Xu
In this paper, we study the convergence behavior of the diffuse domain method (DDM) for solving a class of second-order parabolic partial differential equations with Neumann bounda…