Error estimates of conforming virtual element methods with a modified symmetric Nitsche's formula for 2D semilinear parabolic equations

DOI10.1007/s10915-023-02188-4zbMath1529.65091OpenAlexW4366087619MaRDI QIDQ6101656

Yang Xu, Jingjun Zhao, Zhenguo Zhou

Publication date: 20 June 2023

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-023-02188-4

zbMATH Keywords

semilinear parabolic problemvirtual element methodpolygonal meshmodified Nitsche's method

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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) Semilinear parabolic equations (35K58)

Cites Work

• Unnamed Item
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• Equivalent projectors for virtual element methods
• Virtual element methods for nonlocal parabolic problems on general type of meshes
• On \(L^2\)-error estimate for nonsymmetric interior penalty Galerkin approximation to linear elliptic problems with nonhomogeneous Dirichlet data
• Dirichlet boundary control of semilinear parabolic equations. I: Problems with no state constraints
• Serendipity nodal VEM spaces
• Some error analysis on virtual element methods
• A numerical study of the virtual element method in anisotropic diffusion problems
• A two-level linearized compact ADI scheme for two-dimensional nonlinear reaction-diffusion equations
• Stabilized virtual element methods for the unsteady incompressible Navier-Stokes equations
• A virtual element method for the miscible displacement of incompressible fluids in porous media
• Virtual element methods for the three-field formulation of time-dependent linear poroelasticity
• On the \({H}^1\) conforming virtual element method for time dependent Stokes equation
• Weakly imposed Dirichlet boundary conditions for 2D and 3D virtual elements
• Unconditionally energy stable \(C^0\)-virtual element scheme for solving generalized Swift-Hohenberg equation
• Virtual elements for Maxwell's equations
• High-order interpolatory serendipity virtual element method for semilinear parabolic problems
• Conforming and nonconforming conservative virtual element methods for nonlinear Schrödinger equation: a unified framework
• The virtual element method for resistive magnetohydrodynamics
• Some estimates for virtual element methods
• The nonconforming virtual element method for parabolic problems
• High order VEM on curved domains
• Explicit series solution of travelling waves with a front of Fisher equation
• Virtual Element Method for general second-order elliptic problems on polygonal meshes
• A Penalty-Free Nonsymmetric Nitsche-Type Method for the Weak Imposition of Boundary Conditions
• Virtual element methods for parabolic problems on polygonal meshes
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• Theoretical Numerical Analysis
• A bifurcation problem for a nonlinear partial differential equation of parabolic type^†
• Analysis of a Nonsymmetric Discontinuous Galerkin Method for Elliptic Problems: Stability and Energy Error Estimates
• Conforming and nonconforming virtual element methods for elliptic problems
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• On Traveling Wave Solutions of Fisher's Equation in Two Spatial Dimensions
• Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes
• Virtual element method for semilinear hyperbolic problems on polygonal meshes
• A virtual element discretization for the time dependent Navier–Stokes equations in stream-function formulation
• A virtual element method for a nonlocal FitzHugh–Nagumo model of cardiac electrophysiology
• A Multigrid Method for Unfitted Finite Element Discretizations of Elliptic Interface Problems
• Galerkin Finite Element Methods for Parabolic Problems
• Hybrid high-order discretizations combined with Nitsche’s method for Dirichlet and Signorini boundary conditions
• An Unfitted Hybrid High-Order Method with Cell Agglomeration for Elliptic Interface Problems