Numerical solution of cahn-hilliard system by adaptive least-squares spectral element method

There is a growing interest in the phase-field approach to numerically handle the interface dynamics in multiphase flow phenomena because of its accuracy. The numerical solution of phase-field models has difficulties in dealing with non-self-adjoint operators and the resolution of high gradients within thin interface regions. We present an h-adaptive mesh refinement technique for the least-squares spectral element method for the phase-field models. C 1 Hermite polynomials are used to give global differentiability in the approximated solution, and a space-time coupled formulation and the element-by-element technique are implemented. Two benchmark problems are presented in order to compare two refinement criteria based on the gradient of the solution and the local residual

Numerical solution of cahn-hilliard system by adaptive least-squares spectral element method

There is a growing interest in the phase-field approach to numerically handle the interface dynamics in multiphase flow phenomena because of its accuracy. The numerical solution of phase-field models has difficulties in dealing with non-self-adjoint operators and the resolution of high gradients within thin interface regions. We present an h-adaptive mesh refinement technique for the least-squares spectral element method for the phase-field models. C 1 Hermite polynomials are used to give global differentiability in the approximated solution, and a space-time coupled formulation and the element-by-element technique are implemented. Two benchmark problems are presented in order to compare two refinement criteria based on the gradient of the solution and the local residual.submittedVersionThis is a pre-print of an article published in [Lecture Notes in Computer Science]. The final authenticated version is available online at: https://doi.org/10.1007/978-3-319-73441-5_1