Energy Stable Discontinuous Galerkin Finite Element Method for the Allen–Cahn Equation

DOI10.1142/S0219876218500135zbMath1404.65173arXiv1409.3997MaRDI QIDQ4563130

Ayşe Sarıaydın-Filibelioğlu, Murat Uzunca, Bülent Karasözen, Hamdullah Yücel

Publication date: 6 June 2018

Published in: International Journal of Computational Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.3997

zbMATH Keywords

discontinuous Galerkin methodAllen-Cahn equationgradient systemsunconditional energy stabilitytime adaptivity

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

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Convergence analysis of the fully discrete hybridizable discontinuous Galerkin method for the Allen-Cahn equation based on the invariant energy quadratization approach, An adaptive time-stepping algorithm for the Allen-Cahn equation, A two‐grid finite element method for the Allen‐Cahn equation with the logarithmic potential, Linearly implicit methods for Allen-Cahn equation, Numerical Solution of Some Class of Nonlinear Partial Differential Equations Using Wavelet-Based Full Approximation Scheme, An adaptive discontinuous finite volume element method for the Allen-Cahn equation, Adaptive discontinuous Galerkin finite element methods for the Allen-Cahn equation on polygonal meshes, Numerical error analysis for an energy-stable HDG method for the Allen-Cahn equation, Energy preserving model order reduction of the nonlinear Schrödinger equation, Structure preserving reduced order modeling for gradient systems, A Superconvergent Local Discontinuous Galerkin Method for Nonlinear Fourth-Order Boundary-Value Problems, A Stabilized Finite Volume Element Method for Stationary Stokes–Darcy Equations Using the Lowest Order, A Robust Discontinuous Galerkin High-Order Finite Element Method for Elasticity Problems with Interfaces, Symmetric interior penalty Galerkin method for fractional-in-space phase-field equations

Uses Software

• RODAS

Cites Work

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