Second-order PFEMs for surface diffusion achieve exact area/volume preservation via Simpson-Boole geometric identities on quadratic interpolants without auxiliary multipliers.
Smereka, Semi-implicit level set methods for curvature and surface diffusion motion, Journal of Scientific Com- puting 19 (2003) 439–456
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KFBI-ADI schemes achieve second-order accuracy and unconditional stability for 3D heat equations with irregular boundaries and interfaces, verified numerically and applied to Stefan problems with level sets.
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ADI schemes for heat equations with irregular boundaries and interfaces in 3D with applications
KFBI-ADI schemes achieve second-order accuracy and unconditional stability for 3D heat equations with irregular boundaries and interfaces, verified numerically and applied to Stefan problems with level sets.