Second‐order, fully decoupled, linearized, and unconditionally stable scalar auxiliary variable schemes for <scp>Cahn–Hilliard–Darcy</scp> system
Yali Gao, Xiaoming He, Yufeng Nie
Abstract
Abstract In this paper, we establish the fully decoupled numerical methods by utilizing scalar auxiliary variable approach for solving Cahn–Hilliard–Darcy system. We exploit the operator splitting technique to decouple the coupled system and Galerkin finite element method in space to construct the fully discrete formulation. The developed numerical methods have the features of second order accuracy, totally decoupling, linearization, and unconditional energy stability. The unconditionally stability of the two proposed decoupled numerical schemes are rigorously proved. Abundant numerical results are reported to verify the accuracy and effectiveness of proposed numerical methods.
Topics & Concepts
MathematicsScalar (mathematics)Applied mathematicsDecoupling (probability)LinearizationDiscontinuous Galerkin methodNumerical stabilityGalerkin methodNumerical analysisFinite element methodStability (learning theory)Mathematical analysisNonlinear systemComputer sciencePhysicsGeometryThermodynamicsMachine learningQuantum mechanicsControl engineeringEngineeringSolidification and crystal growth phenomenaDifferential Equations and Numerical MethodsAdvanced Numerical Methods in Computational Mathematics