Weak Galerkin finite element method for the parabolic integro-differential equation with weakly singular kernel

DOI10.1007/s40314-019-0807-7zbMath1438.65303OpenAlexW2918713809WikidataQ115373850 ScholiaQ115373850MaRDI QIDQ2322420

Yanyan Li

Publication date: 4 September 2019

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

Full work available at URL: https://doi.org/10.1007/s40314-019-0807-7

zbMATH Keywords

stabilityconvergencenumerical experimentbackward Euler schemeparabolic integro-differential equationweak Galerkin finite element method

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Variational methods for elliptic systems (35J50) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Integro-partial differential equations (35R09)

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Cites Work

• Unnamed Item
• Orthogonal spline collocation method for the two-dimensional fractional sub-diffusion equation
• Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion
• A weak finite element method for elliptic problems in one space dimension
• A finite difference scheme for partial integro-differential equations with a weakly singular kernel
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• A new computational approach for solving nonlinear local fractional PDEs
• A weak Galerkin finite element method for second-order elliptic problems
• A new fractional operator of variable order: application in the description of anomalous diffusion
• Discrete-time orthogonal spline collocation method with application to two-dimensional fractional cable equation
• A Compact Difference Scheme for an Evolution Equation with a Weakly Singular Kernel
• Weak Galerkin finite element methods for Parabolic equations
• On L² Error Estimate for Weak Galerkin Finite Element Methods for Parabolic Problems
• A Difference Scheme for a Nonlinear Partial Integrodifferential Equation
• A Space-Time Spectral Method for the Time Fractional Diffusion Equation
• Finite Element Approximation of a Parabolic Integro-Differential Equation with a Weakly Singular Kernel
• Numerical solution of an evolution equation with a positive-type memory term
• A space‐time spectral collocation method for the 2‐dimensional nonlinear Riesz space fractional diffusion equations
• The BDF orthogonal spline collocation method for the two-dimensional evolution equation with memory
• A Priori $L_2 $ Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations

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