An $\alpha$-robust and new two-grid nonuniform L2-1$_\sigma$ FEM for nonlinear time-fractional diffusion equation (Q6647619)

scientific article; zbMATH DE number 7953249

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English	An $\alpha$-robust and new two-grid nonuniform L2-1$_\sigma$ FEM for nonlinear time-fractional diffusion equation	scientific article; zbMATH DE number 7953249

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scholarly article

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title

An $\alpha$-robust and new two-grid nonuniform L2-1$_\sigma$ FEM for nonlinear time-fractional diffusion equation (English)

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author

Zhijun Tan

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publication date

3 December 2024

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zbMATH Keywords

two-grid FEM

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nonlinear time-fractional diffusion equation

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nonuniform L2-1$_\sigma$ scheme

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$\alpha$-robust analysis

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Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations

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Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation

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A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems

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Error analysis of an L2-type method on graded meshes for a fractional-order parabolic problem

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Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions

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Convergence analysis of the anisotropic FEM for 2D time fractional variable coefficient diffusion equations on graded meshes

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Optimal spatial $H^1$-norm analysis of a finite element method for a time-fractional diffusion equation

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Sharp $H^1$-norm error estimates of two time-stepping schemes for reaction-subdiffusion problems

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$ \alpha $-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation

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A sharp $\alpha$-robust $L^\infty (H^1)$ error bound for a time-fractional Allen-Cahn problem discretised by the Alikhanov $L2-1_\sigma$ scheme and a standard FEM

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A Second-Order Scheme with Nonuniform Time Steps for a Linear Reaction-Subdiffusion Problem

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Direct discontinuous Galerkin method for solving nonlinear time fractional diffusion equation with weak singularity solution

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Unconditional convergence of a fast two-level linearized algorithm for semilinear subdiffusion equations

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Positive definiteness of real quadratic forms resulting from the variable-step $\mathrm{L}1$-type approximations of convolution operators

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Energy stability of variable-step L1-type schemes for time-fractional Cahn-Hilliard model

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Discrete Gradient Structure of a Second-Order Variable-Step Method for Nonlinear Integro-Differential Models

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Asymptotically compatible energy and dissipation law of the nonuniform L2-$1_{\sigma}$ scheme for time fractional Allen-Cahn model

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High-order energy stable variable-step schemes for the time-fractional Cahn-Hilliard model

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Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations

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Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations: A Second-Order Scheme

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Unconditionally optimal $H^1$-norm error estimates of a fast and linearized Galerkin method for nonlinear subdiffusion equations

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Unconditionally optimal $H^1$-error estimate of a fast nonuniform $\mathrm{L}2-1_\sigma$ scheme for nonlinear subdiffusion equations

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A Fast High Order Method for the Time-Fractional Diffusion Equation

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Error analysis of a high order method for time-fractional diffusion equations

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A new difference scheme for the time fractional diffusion equation

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High-order Time Stepping Schemes for Semilinear Subdiffusion Equations

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Two-Grid Discretization Techniques for Linear and Nonlinear PDE<scp>s</scp>

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A two-grid mixed finite element method for a nonlinear fourth-order reaction-diffusion problem with time-fractional derivative

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A two-grid finite element approximation for a nonlinear time-fractional Cable equation

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Two-grid methods for nonlinear time fractional diffusion equations by $L 1$-Galerkin FEM

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A two-grid MMOC finite element method for nonlinear variable-order time-fractional mobile/immobile advection-diffusion equations

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Fast calculation based on a spatial two‐grid finite element algorithm for a nonlinear space–time fractional diffusion model

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Efficient Application of the Two-Grid Technique for Solving Time-Fractional Non-linear Parabolic Problem

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A two-grid block-centered finite difference method for the nonlinear time-fractional parabolic equation

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An Improved Two-Grid Technique for the Nonlinear Time-Fractional Parabolic Equation Based on the Block-Centered Finite Difference Method

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Two-grid methods for semilinear time fractional reaction diffusion equations by expanded mixed finite element method

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Superconvergence analysis of a two-grid finite element method for nonlinear time-fractional diffusion equations

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Two finite difference schemes for time fractional diffusion-wave equation

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

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Two-grid finite element methods for nonlinear time-fractional parabolic equations

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Two-grid fully discrete finite element algorithms on temporal graded meshes for nonlinear multi-term time-fractional diffusion equations with variable coefficient

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$\alpha$-robust analysis of fast and novel two-grid FEM with nonuniform $\mathrm{L}1$ scheme for semilinear time-fractional variable coefficient diffusion equations

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A high-order two-grid difference method for nonlinear time-fractional biharmonic problems and its unconditional $\alpha$-robust error estimates

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Q5576913

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The Mathematical Theory of Finite Element Methods

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Error analysis of a second-order method on fitted meshes for a time-fractional diffusion problem

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A second-order fast compact scheme with unequal time-steps for subdiffusion problems

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An $\alpha $-robust finite element method for a multi-term time-fractional diffusion problem

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Blow-up of error estimates in time-fractional initial-boundary value problems

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$ \alpha $-robust $H^1$-norm error estimate of nonuniform Alikhanov scheme for fractional sub-diffusion equation

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Galerkin Finite Element Methods for Parabolic Problems

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published in

Computers & Mathematics with Applications

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.CAMWA.2024.10.023

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Mathematics(1 entry)

mardi Publication:6647619

An \(\alpha\)-robust and new two-grid nonuniform L2-1\(_\sigma\) FEM for nonlinear time-fractional diffusion equation (Q6647619)

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Mathematics(1 entry)