A new energy-stable nonconforming finite element method for Sobolev equation with Burgers' type nonlinearity. (January 2023)

• Record Type: Journal Article
• Authors: Wang, Junjun; Li, Meng; Li, Xi
• Is Part Of: Applied mathematics letters. Volume 135(2023)
• Publication Date: 2023-01
• Subjects: Sobolev equation with Burgers' type nonlinearity -- Nonconforming FEM -- Energy dissipation -- Superconvergence analysis; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2022.108440
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We propose an energy-stable finite element method (FEM) of the Sobolev equation with Burgers' type nonlinearity by implicit Euler method in time and nonconforming E Q 1 r o t element in space. A stabilized term is innovatively added in this work to preserve the energy dissipation of the numerical scheme. Then we directly obtain the prior estimates of the numerical solution, with which the unique solvability of the fully-discrete scheme is derived. Subsequently, a novel strategy is utilized to achieve the superclose estimate of order O ( h 2 + τ ) in broken H 1 -norm. Using the interpolated postprocessing technique, the global superconvergence result is obtained. At last, numerical example is given to confirm the theoretical analysis. Here, h is the spatial parameter, and τ is the time step.