Numerical analysis of a FE/SAV scheme for a Caginalp phase field model with mechanical effects in stereolithography

Abstract

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.