Geodesic
Numerical analysis of a FE/SAV scheme for a Caginalp phase field model with mechanical effects in stereolithography
Xingguang Jin1 orcid ; Kei Fong Lam2 orcid ; Changqing Ye1 orcid
1The Chinese University of Hong Kong, Shatin, Hong Kong
2Hong Kong Baptist University, Kowloon Tong, Hong Kong
Interfaces and free boundaries, Tome 27 (2025) no. 3, pp. 469-520

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DOI

In this work, we propose a phase field model based on a Caginalp system with mechanical effects to study the underlying physical and chemical processes behind stereolithography, which is an additive manufacturing (3D printing) technique that builds objects in a layer-by-layer fashion by using an ultraviolet laser to solidify liquid polymer resins. Existence of weak solutions is established by demonstrating the convergence of a numerical scheme based on a first order scalar auxiliary variable temporal discretization and a finite element spatial discretization. We further establish uniqueness and regularity of solutions, as well as optimal error estimates for the Caginalp system that are supported by numerical simulations. We also present some qualitative two-dimensional simulations of the stereolithography processes captured by the model.
DOI : 10.4171/ifb/539
Classification : 35K35, 35K58, 65M12, 65M15, 74B05
Mots-clés : stereolithography, 3D printing, scalar auxiliary variable, Caginalp phase field system, finite element discretization, convergence analysis

Xingguang Jin  1   ; Kei Fong Lam  2   ; Changqing Ye  1

1 The Chinese University of Hong Kong, Shatin, Hong Kong
2 Hong Kong Baptist University, Kowloon Tong, Hong Kong 
Xingguang Jin; Kei Fong Lam; Changqing Ye. Numerical analysis of a FE/SAV scheme for a Caginalp phase field model with mechanical effects in stereolithography. Interfaces and free boundaries, Tome 27 (2025) no. 3, pp. 469-520. doi: 10.4171/ifb/539
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     title = {Numerical analysis of a {FE/SAV} scheme for a {Caginalp} phase field model with mechanical effects in stereolithography},
     journal = {Interfaces and free boundaries},
     pages = {469--520},
     year = {2025},
     volume = {27},
     number = {3},
     doi = {10.4171/ifb/539},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/539/}
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