A novel two-grid Crank-Nicolson mixed finite element method for nonlinear fourth-order sin-Gordon equation

• DOI: 10.3934/math.20241515
• Publication Date: 2024-11-05T10:16:08Z
• Authors: Yanjie Zhou; Xianxiang Leng; Yuejie Li; Qiuxiang Deng; Zhendong Luo
• Keywords: Crank–Nicolson method

<p>A new nonlinear fourth-order sin-Gordon equation with actual physical background is first created. Then, by introducing an auxiliary function, the decomposed into system of equations second-order derivatives spatial variables. Subsequently, time derivative discretized using Crank-Nicolson (CN) scheme to construct a semi-discretized mixed CN (TSDMCN) scheme. Thereafter, variables in TSDMCN are two-grid finite element (MFE) method MFE (TGCNMFE) unconditional stability and precision, which consists defined on coarser grids linear finer sufficiently high very easy solve. The existence, stability, error estimates TGCNMFE solutions strictly proved theoretically, superiorities correctness theoretical results verified two sets numerical experiments.</p>