Super-Closeness between the Ritz Projection and the Finite Element Solution for some Elliptic Problems

DOI10.4208/cicp.OA-2019-0154zbMath1474.65444OpenAlexW3033828164MaRDI QIDQ5162318

Wenbin Chen, Yanqiu Wang, Ruosi Liang, Yue Yan

Publication date: 2 November 2021

Published in: Communications in Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/cicp.oa-2019-0154

zbMATH Keywords

finite elementRitz projectionnegative norm estimatesuper-closeness estimate

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Higher-order elliptic equations (35J30)

Uses Software

• iFEM

Cites Work

• Unnamed Item
• An efficient and long-time accurate third-order algorithm for the Stokes-Darcy system
• Error analysis of a mixed finite element method for a Cahn-Hilliard-Hele-Shaw system
• Galerkin finite element methods for parabolic problems
• Finite element approximation of a fourth order nonlinear degenerate parabolic equation
• Implicit time splitting for fourth-order parabolic equations
• A fourth-order parabolic equation modeling epitaxial thin film growth
• A second order energy stable scheme for the Cahn-Hilliard-Hele-Shaw equations
• A second order energy stable linear scheme for a thin film model without slope selection
• Superconvergence in Galerkin finite element methods
• Optimal convergence analysis of a second order scheme for a thin film model without slope selection
• Uniquely solvable and energy stable decoupled numerical schemes for the Cahn-Hilliard-Stokes-Darcy system for two-phase flows in karstic geometry
• Convergence analysis of a fully discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equation
• A Second Order BDF Numerical Scheme with Variable Steps for the Cahn--Hilliard Equation
• A Second-Order Energy Stable BDF Numerical Scheme for the Cahn-Hilliard Equation
• Optimal Convergence Analysis of a Mixed Finite Element Method for Fourth-Order Elliptic Problems
• New epitaxial thin‐film models and numerical approximation
• Analyses and Applications of the Second-Order Cross Correlation in the Passive Imaging
• Optimal convergence analysis of mixed finite element methods for fourth-order elliptic and parabolic problems