The phase field method for geometric moving interfaces and their numerical approximations
By Qiang Du, Xiaobing H. Feng. Geometric Partial Differential Equations - Part I, 2019
158 citations recorded by the source corpus.
Abstract This chapter surveys recent numerical advances in the phase field method for geometric surface evolution and related geometric nonlinear partial differential equations (PDEs). Instead of describing technical details of various numerical methods and their analyses, the chapter presents a holistic overview about the main ideas of phase field modelling, its mathematical foundation, and relationships between the phase field formalism and other mathematical formalisms for geometric moving interface problems, as well as the current state of the art of numerical approximations of various phase field models with an emphasis on discussing the main ideas of numerical analysis techniques. The chapter also reviews recent development on adaptive grid methods and various applications of the phase field modelling and their numerical methods in materials science, fluid mechanics, biology and image science.
Subfields: Computational Mechanics, Computational Theory and Mathematics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/cfe582aa454de2cac529322cd2292ba283e58ae9
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In Computational Mechanics
In Computational Theory and Mathematics
In Materials Chemistry
Citations in the corpus
- A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, background): “This approach has several advantages, see e.g., [6, 7].”