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Numerical analysis of a second-order energy-stable finite element method for the Swift-Hohenberg equation

Published: 04 March 2024 Publication History

Abstract

In this work, we first prove the existence, uniqueness and regularity of the solution of the Swift-Hohenberg equation by applying the Galerkin spectral method. Then we investigate the convergence of a finite element method in the mixed formulation for the Swift-Hohenberg equation, with Crank-Nicolson scheme in time discretization. We prove that our semidiscrete and fully discrete numerical schemes satisfy unique solvability and unconditional energy stability. Moreover, we prove optimal error estimates for the schemes. Finally, numerical tests are given to validate our theoretical results.

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            Published In

            cover image Applied Numerical Mathematics
            Applied Numerical Mathematics  Volume 197, Issue C
            Mar 2024
            389 pages

            Publisher

            Elsevier Science Publishers B. V.

            Netherlands

            Publication History

            Published: 04 March 2024

            Author Tags

            1. Swift-Hohenberg equation
            2. Optimal error estimates
            3. Finite element method
            4. Crank-Nicolson scheme

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