\(L^{2}\) error estimate of the finite volume element methods on quadrilateral meshes
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Publication:983691
DOI10.1007/s10444-009-9121-zzbMath1198.65218OpenAlexW2093179496MaRDI QIDQ983691
Publication date: 24 July 2010
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10444-009-9121-z
convergencePoisson equationquadrilateral meshesfinite volume element methods\(L ^{2}\) error estimateisoparametric bilinear element
Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Finite volume methods for boundary value problems involving PDEs (65N08)
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Cites Work
- Unnamed Item
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- Unnamed Item
- Unnamed Item
- Unnamed Item
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- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the finite volume element method
- A convergence condition for the quadrilateral Wilson element
- On first and second order box schemes
- Box schemes on quadrilateral meshes
- A note on the optimal \(L^2\)-estimate of the finite volume element method
- A finite volume method based on the Crouzeix-Raviart element for elliptic PDE's in two dimensions
- High order finite volume methods for singular perturbation problems
- The finite volume element method with quadratic basis functions
- A second-order finite volume element method on quadrilateral meshes for elliptic equations
- Finite Element Methods for Navier-Stokes Equations
- Some Error Estimates for the Box Method
- Convergence of Finite Volume Schemes for Poisson’s Equation on Nonuniform Meshes
- Theory of a Finite Difference Method on Irregular Networks
- On the Finite Volume Element Method for General Self-Adjoint Elliptic Problems
- Error estimates for finite volume element methods for general second-order elliptic problems
- On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials
- On the Construction and Analysis of High Order Locally Conservative Finite Volume-Type Methods for One-Dimensional Elliptic Problems
- Error estimates in $L^2$, $H^1$ and $L^\infty$ in covolume methods for elliptic and parabolic problems: A unified approach
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