A new approach of superconvergence analysis of nonconforming Wilson finite element for semi-linear parabolic problem

DOI10.1016/j.camwa.2021.04.022OpenAlexW3159707411MaRDI QIDQ2027597

Xiangyu Shi, Lin-Zhang Lu

Publication date: 27 May 2021

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2021.04.022

zbMATH Keywords

DGMsemi-linear parabolic problemnonconforming Wilson elementsemi- and fully-discrete schemessuperconvergent estimates

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items

Unconditional optimal error estimates of a modified finite element fully discrete scheme for the complex Ginzburg-Landau equation ⋮ Unconditional superconvergence analysis of two modified finite element fully discrete schemes for nonlinear Burgers' equation ⋮ Convergence and superconvergence analysis of a nonconforming finite element variable-time-step BDF2 implicit scheme for linear reaction-diffusion equations

Cites Work

• Unnamed Item
• Unnamed Item
• Superconvergence of an \(H^1\)-Galerkin nonconforming mixed finite element method for a parabolic equation
• Unconditional superconvergence analysis for nonlinear parabolic equation with \(EQ_1^{rot}\) nonconforming finite element
• Superconvergence analysis and error expansion for the Wilson nonconforming finite element
• A new superconvergence property of Wilson nonconforming finite element
• Superconvergence analysis of a two-grid method for semilinear parabolic equations
• A nonconforming scheme to solve the parabolic problem
• Unconditional optimal error estimates of a two-grid method for semilinear parabolic equation
• Superconvergence analysis of high-order rectangular edge elements for time-harmonic Maxwell's equations
• Superconvergence analysis of the lowest order rectangular Raviart-Thomas element for semilinear parabolic equation
• Superconvergence analysis of two-grid finite element method for nonlinear Benjamin-Bona-Mahony equation
• Superconvergent recovery of edge finite element approximation for Maxwell's equations
• A new two-grid nonconforming mixed finite element method for nonlinear Benjamin-Bona-Mahoney equation
• Nonconforming quadrilateral finite element method for a class of nonlinear sine-Gordon equations
• Weak Galerkin finite element methods for Parabolic equations
• Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusion Equations in One Space Dimension
• Superconvergence of Local Discontinuous Galerkin methods for one-dimensional linear parabolic equations
• Analysis of Sharp Superconvergence of Local Discontinuous Galerkin Method for One-Dimensional Linear Parabolic Equations
• Unconditionally Superclose Analysis of a New Mixed Finite Element Method for Nonlinear Parabolic Equation
• Approximation of Nonconforming Quasi-Wilson Element for Sine-Gordon Equations
• Galerkin Finite Element Methods for Parabolic Problems