Triangulation-based isogeometric analysis of the Cahn–Hilliard phase-field model.

This paper presents triangulation-based Isogeometric Analysis of the Cahn–Hilliard phase-field model. The Cahn–Hilliard phase-field model is governed by a time-dependent fourth-order partial differential equation. The corresponding primal variational form involves second-order operators, making it difficult to be directly analyzed with traditional C 0 finite element analysis. In this paper, we construct C 1 Bernstein–Bézier simplicial elements through macro-element techniques, including various triangle-split based macro-elements in both 2D and 3D space. We extend triangulation-based isogeometric analysis to solving the primal variational form of the Cahn–Hilliard equation. We validate our method by convergence analysis, showing the nodal and degree-of-freedom advantages over C 0 Finite Element Analysis. We then demonstrate detailed system evolution from randomly perturbed initial conditions in periodic two-dimensional squares and three-dimensional cubes. We incorporate an adaptive time-stepping scheme in these numerical experiments. Our numerical study demonstrates that triangulation-based isogeometric analysis offers optimal convergence and time step stability, is applicable to complex geometry and allows local refinement. • We use triangular macro-elements for C1 smoothness, rather than Lagrange multipliers. • Our construction of C1 elements is automatic. • Our approach is applicable to problems domains of complex topology. • Our approach allows convenient local refinement. • We have achieved optimal convergence rates for a model problem. [ABSTRACT FROM AUTHOR]