Two-grid finite element methods for nonlinear time fractional variable coefficient diffusion equations

Zeng, Yunhua; Tan, Zhijun

doi:10.1016/j.amc.2022.127408

Applied Mathematics and Computation

2022

DOI: 10.1016/j.amc.2022.127408

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Two-grid finite element methods for nonlinear time fractional variable coefficient diffusion equations

Yunhua Zeng

Zhijun Tan

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Cited by 3 publications

References 41 publications

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Pointwise-in-time $ \alpha $-robust error estimate of the ADI difference scheme for three-dimensional fractional subdiffusion equations with variable coefficients

Xiao,

Yang,

Zhou

2024

CAM

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<abstract>In this paper, a fully-discrete alternating direction implicit (ADI) difference method is proposed for solving three-dimensional (3D) fractional subdiffusion equations with variable coefficients, whose solution presents a weak singularity at $ t = 0 $. The proposed method is established via the L1 scheme on graded mesh for the Caputo fractional derivative and central difference method for spatial derivative, and an ADI method is structured to change the 3D problem into three 1D problems. Using the modified Grönwall inequality we prove the stability and $ \alpha $-robust convergence. The results presented in numerical experiments are in accordance with the theoretical analysis.</abstract>

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Pointwise-in-time $ \alpha $-robust error estimate of the ADI difference scheme for three-dimensional fractional subdiffusion equations with variable coefficients

Xiao,

Yang,

Zhou

2024

CAM

View full text Add to dashboard Cite

show abstract

Two-grid $ H^1 $-Galerkin mixed finite elements combined with $ L1 $ scheme for nonlinear time fractional parabolic equations

Pan,

Tang

2023

era

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<abstract>In this paper, we propose a two-grid algorithm for nonlinear time fractional parabolic equations by $ H^1 $-Galerkin mixed finite element discreitzation. First, we use linear finite elements and Raviart-Thomas mixed finite elements for spatial discretization, and $ L1 $ scheme on graded mesh for temporal discretization to construct a fully discrete approximation scheme. Second, we derive the stability and error estimates of the discrete scheme. Third, we present a two-grid method to linearize the nonlinear system and discuss its stability and convergence. Finally, we confirm our theoretical results by some numerical examples.</abstract>

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A two-grid ADI finite element approximation for a nonlinear distributed-order fractional sub-diffusion equation

Hou

Cao

Liu

et al. 2023

NHM

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<abstract>In this paper, a two-grid alternating direction implicit (ADI) finite element (FE) method based on the weighted and shifted Grünwald difference (WSGD) operator is proposed for solving a two-dimensional nonlinear time distributed-order fractional sub-diffusion equation. The stability and optimal error estimates with second-order convergence rate in spatial direction are obtained. The storage space can be reduced and computing efficiency can be improved in this method. Two numerical examples are provided to verify the theoretical results.</abstract>

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Two-grid finite element methods for nonlinear time fractional variable coefficient diffusion equations

Cited by 3 publications

References 41 publications

Pointwise-in-time $ \alpha $-robust error estimate of the ADI difference scheme for three-dimensional fractional subdiffusion equations with variable coefficients

Pointwise-in-time $ \alpha $-robust error estimate of the ADI difference scheme for three-dimensional fractional subdiffusion equations with variable coefficients

Two-grid $ H^1 $-Galerkin mixed finite elements combined with $ L1 $ scheme for nonlinear time fractional parabolic equations

A two-grid ADI finite element approximation for a nonlinear distributed-order fractional sub-diffusion equation

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