An \(h\)-\(p\) Petrov-Galerkin finite element method for linear Volterra integro-differential equations
From MaRDI portal
Publication:487493
DOI10.1007/s11425-014-4805-3zbMath1311.65172OpenAlexW2014617375MaRDI QIDQ487493
Publication date: 22 January 2015
Published in: Science China. Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11425-014-4805-3
Petrov-Galerkin methodVolterra integro-differential equationstime-stepping scheme\(h\)-\(p\) finite element method
Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Volterra integral equations (45D05) Linear integral equations (45A05)
Related Items
Exponential convergence of the \textit{hp}-version of the composite Gauss-Legendre quadrature for integrals with endpoint singularities ⋮ An $h$-$p$ Version of the Continuous Petrov--Galerkin Finite Element Method for Volterra Integro-Differential Equations with Smooth and Nonsmooth Kernels ⋮ Superconvergence and postprocessing of the continuous Galerkin method for nonlinear Volterra integro-differential equations ⋮ Superconvergent postprocessing of the discontinuous Galerkin time stepping method for nonlinear Volterra integro-differential equations ⋮ An \(h-p\) version of the continuous Petrov-Galerkin finite element method for nonlinear Volterra integro-differential equations ⋮ A feedforward neural network based on Legendre polynomial for solving linear Fredholm integro-differential equations ⋮ An $hp$-version Legendre-Jacobi spectral collocation method for Volterra integro-differential equations with smooth and weakly singular kernels ⋮ Numerical solution of nonlinear weakly singular Volterra integral equations of the first kind: an \textit{hp}-version collocation approach ⋮ \(hp\)-version collocation method for a class of nonlinear Volterra integral equations of the first kind ⋮ An \(hp\)-version of the \(C^0\)-continuous Petrov-Galerkin method for second-order Volterra integro-differential equations ⋮ The efficient alternating direction implicit Galerkin method for the nonlocal diffusion-wave equation in three dimensions
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Stability of the difference type methods for linear Volterra equations in Hilbert spaces
- Legendre and Chebyshev dual-Petrov-Galerkin methods for hyperbolic equations
- An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable
- An analysis of the Petrov - Galerkin finite element method
- Superconvergence of numerical solutions to weakly singular Volterra integro-differential equations
- On spectral methods for Volterra-type integro-differential equations
- An \textit{a priori} error analysis of the \(hp\)-version of the continuous Galerkin FEM for nonlinear initial value problems
- A Note on Jacobi Spectral-Collocation Methods for Weakly Singular Volterra Integral Equations with Smooth Solutions
- Spectral Petrov-Galerkin Methods for the Second Kind Volterra Type Integro-Differential Equations
- Uniform l1 behaviour in a second-order difference-type method for a linear Volterra equation with completely monotonic kernel I: stability
- An $hp$-Version Discontinuous Galerkin Method for Integro-Differential Equations of Parabolic Type
- Implicit Runge-Kutta Methods of Optimal Order for Volterra Integro-Differential Equations
- Polynomial Spline Collocation Methods for Volterra Integrodifferential Equations with Weakly Singular Kernels
- A note on collocation methods for Volterra integro-differential equations with weakly singular kernels
- Petrov--Galerkin Methods for Linear Volterra Integro-Differential Equations
- Global error control for the continuous Galerkin finite element method for ordinary differential equations
- Collocation Methods for Volterra Integral and Related Functional Differential Equations
- Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions
- hp-Discontinuous Galerkin Time-Stepping for Volterra Integrodifferential Equations
