A C0 interior penalty method for the phase field crystal equation

DOI10.1002/num.22976arXiv2011.08937OpenAlexW3098545116MaRDI QIDQ6086381

Natasha Sharma, Amanda E. Diegel

Publication date: 12 December 2023

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.08937

zbMATH Keywords

finite element methodnonlinear partial differential equationenergy stabilityhigher-order methodsphase field crystal\(\mathrm{C}^0\) Interior penalty methodsixth-order parabolic

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

Cites Work

• Unnamed Item
• An unconditionally energy-stable method for the phase field crystal equation
• An adaptive time-stepping strategy for solving the phase field crystal model
• \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
• A robust WG finite element method for convection-diffusion-reaction equations
• Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation
• Convergence analysis of an adaptive interior penalty discontinuous Galerkin method for the biharmonic problem
• First and second order numerical methods based on a new convex splitting for phase-field crystal equation
• Convergence analysis and numerical implementation of a second order numerical scheme for the three-dimensional phase field crystal equation
• Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity
• Analysis of an interior penalty method for fourth order problems on polygonal domains
• A fully discrete \(C^0\) interior penalty Galerkin approximation of the extended Fisher-Kolmogorov equation
• Splitting schemes for phase-field models
• Post-processing procedures for an elliptic distributed optimal control problem with pointwise state constraints
• Two-level additive Schwarz preconditioners for \(C^0\) interior penalty methods
• C 0 Interior Penalty Methods
• Analysis of a Mixed Finite Element Method for a Cahn--Hilliard--Darcy--Stokes System
• A $\mathcal{C}^0$ Interior Penalty Method for a Fourth Order Elliptic Singular Perturbation Problem
• An interior penalty method for a sixth-order elliptic equation
• A Quadratic $C^0$ Interior Penalty Method for Linear Fourth Order Boundary Value Problems with Boundary Conditions of the Cahn--Hilliard Type
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation
• An a posteriori error estimator for a quadratic C0-interior penalty method for the biharmonic problem
• A Nonconforming Finite-Element Method for the Two-Dimensional Cahn–Hilliard Equation
• Poincaré–Friedrichs Inequalities for PiecewiseH²Functions
• A Quadratic $C^0$ Interior Penalty Method for the Displacement Obstacle Problem of Clamped Kirchhoff Plates
• On a Class of Cahn--Hilliard Models with Nonlinear Diffusion
• C $$^0$$ -Interior Penalty Discontinuous Galerkin Approximation of a Sixth-Order Cahn-Hilliard Equation Modeling Microemulsification Processes
• A Quadratic C 0 Interior Penalty Method for an Elliptic Optimal Control Problem with State Constraints
• Multigrid Algorithms for C0 Interior Penalty Methods

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