A virtual element method for the wave equation on curved edges in two dimensions

DOI10.1007/s10915-021-01683-wzbMath1489.65139arXiv2106.06314OpenAlexW3166757847MaRDI QIDQ2063173

Alessio Fumagalli, Anna Scotti, Giuseppe Vacca, Franco Dassi, Ilario Mazzieri

Publication date: 10 January 2022

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

Full work available at URL: https://arxiv.org/abs/2106.06314

zbMATH Keywords

wave equationcurved elementsvirtual element methodpolygonal grids

Mathematics Subject Classification ID

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) 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)

Related Items (5)

Bend 3D mixed virtual element method for Darcy problems ⋮ On the Coupling of the Curved Virtual Element Method with the One-Equation Boundary Element Method for 2D Exterior Helmholtz Problems ⋮ Virtual element methods for weakly damped wave equations on polygonal meshes ⋮ A cVEM-DG space-time method for the dissipative wave equation ⋮ The nonconforming virtual element method with curved edges

Cites Work

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• Equivalent projectors for virtual element methods
• A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media
• Assessment of hybrid high-order methods on curved meshes and comparison with discontinuous Galerkin methods
• Fast numerical integration on polytopic meshes with applications to discontinuous Galerkin finite element methods
• Discontinuous Galerkin methods for acoustic wave propagation in polygons
• High-order virtual element method on polyhedral meshes
• The virtual element method for discrete fracture network simulations
• A posteriori error estimates for the virtual element method
• An \(hp\)-hybrid high-order method for variable diffusion on general meshes
• Multigrid algorithms for \(hp\)-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes
• A hybrid high-order method for the steady incompressible Navier-Stokes problem
• High-order discontinuous Galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes
• A high-order discontinuous Galerkin approach to the elasto-acoustic problem
• Curvilinear virtual elements for 2D solid mechanics applications
• A high-order discontinuous Galerkin method for nonlinear sound waves
• The mixed virtual element method on curved edges in two dimensions
• Hybrid high-order methods for variable-diffusion problems on general meshes
• High order VEM on curved domains
• The Stokes complex for virtual elements with application to Navier-Stokes flows
• Implicit spectral element methods and Neumann-Neumann preconditioners for acoustic waves
• The mimetic finite difference method for elliptic problems
• Virtual Element Method for general second-order elliptic problems on polygonal meshes
• Gradient schemes: Generic tools for the numerical analysis of diffusion equations
• Mimetic finite difference approximation of flows in fractured porous media
• The nonconforming virtual element method
• Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains
• A Parallel Spectral Element Method for Acoustic Wave Modeling
• A $C^1$ Virtual Element Method for the Cahn--Hilliard Equation with Polygonal Meshes
• Optimal Isoparametric Finite Elements and Error Estimates for Domains Involving Curved Boundaries
• A Hybrid High-Order Method for Nonlinear Elasticity
• Isogeometric Analysis
• The fully nonconforming virtual element method for biharmonic problems
• A Hybrid High-Order Method for Darcy Flows in Fractured Porous Media
• Conforming and nonconforming virtual element methods for elliptic problems
• A Family of Three-Dimensional Virtual Elements with Applications to Magnetostatics
• Absorbing boundary conditions for the wave equation and parallel computing
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• Polynomial preserving virtual elements with curved edges
• Mimetic finite differences for nonlinear and control problems
• The Hitchhiker's Guide to the Virtual Element Method
• The Virtual Element Method with curved edges
• CONVERGENCE OF MIMETIC FINITE DIFFERENCE METHOD FOR DIFFUSION PROBLEMS ON POLYHEDRAL MESHES WITH CURVED FACES
• hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes
• A Stream Virtual Element Formulation of the Stokes Problem on Polygonal Meshes
• The Mathematical Theory of Finite Element Methods
• Discontinuous Galerkin Finite Element Method for the Wave Equation
• A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES
• An Unfitted Hybrid High-Order Method with Cell Agglomeration for Elliptic Interface Problems

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