Cubic superconvergent finite volume element method for one-dimensional elliptic and parabolic equations

DOI10.1016/j.cam.2009.10.013zbMath1197.65171OpenAlexW1988386904MaRDI QIDQ847180

Tongke Wang, Guang-hua Gao

Publication date: 12 February 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.10.013

zbMATH Keywords

error estimatesfinite volume methodnumerical examplesparabolic equationsuperconvergenceelliptic equationcubic interpolationmixed Dirichlet and Robin boundary conditionsoptimal stress point

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Initial-boundary value problems for second-order parabolic equations (35K20) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (9)

Superconvergence analysis for a nonlinear parabolic equation with a BDF finite element method ⋮ Higher‐order finite volume element methods based on Barlow points for one‐dimensional elliptic and parabolic problems ⋮ Superconvergence analysis for nonlinear parabolic equation with \(EQ_1^{\mathrm{rot}}\) nonconforming finite element ⋮ A Quadratic Finite Volume Method for Parabolic Problems ⋮ \(L^{2}\) error estimation of a quadratic finite volume element method for pseudo-parabolic equations in three spatial dimensions ⋮ Biquadratic finite volume element methods based on optimal stress points for parabolic problems ⋮ Some recent advances on vertex centered finite volume element methods for elliptic equations ⋮ Unconditional superconvergence analysis for nonlinear parabolic equation with \(EQ_1^{rot}\) nonconforming finite element ⋮ A high order finite volume method for one dimensional nonlocal reactive flows of parabolic type

Cites Work

• Analysis of linear and quadratic simplicial finite volume methods for elliptic equations
• Error estimation of a quadratic finite volume method on right quadrangular prism grids
• Development and analysis of higher order finite volume methods over rectangles for elliptic equations
• A mixed finite volume element method based on rectangular mesh for biharmonic equations
• Two-grid finite volume element method for linear and nonlinear elliptic problems
• A second-order finite volume element method on quadrilateral meshes for elliptic equations
• On the Accuracy of the Finite Volume Element Method for Diffusion Equations on Composite Grids
• Discretization methods with analytical characteristic methods for advection-diffusion-reaction equations and 2d applications
• Convergence of Finite Volume Schemes for Poisson’s Equation on Nonuniform Meshes
• Lp error estimates and superconvergence for covolume or finite volume element methods
• High-order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD
• Error estimates for finite volume element methods for general second-order elliptic problems
• Error estimates for a finite volume element method for parabolic equations in convex polygonal domains
• On the Construction and Analysis of High Order Locally Conservative Finite Volume-Type Methods for One-Dimensional Elliptic Problems
• Error Estimates for a Finite Volume Element Method for Elliptic PDEs in Nonconvex Polygonal Domains
• Error estimates in $L^2$, $H^1$ and $L^\infty$ in covolume methods for elliptic and parabolic problems: A unified approach
• Alternating direction finite volume element methods for 2D parabolic partial differential equations
• Analysis of the cell-centred finite volume method for the diffusion equation
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