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

https://doi.org/10.1093/imanum/draa015
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Galerkin Finite Element Methods for Parabolic Problems
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The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type
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Optimal Error Analysis of a FEM for Fractional Diffusion Problems by Energy Arguments
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A Fitted Scheme for a Caputo Initial-Boundary Value Problem
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Error Analysis of a Second-Order Method on Fitted Meshes for a Time-Fractional Diffusion Problem
inferredcites →https://doi.org/10.1007/s11075-016-0106-yopenalex-snapshot
A discontinuous Galerkin method for time fractional diffusion equations with variable coefficients
inferredcites →https://doi.org/10.1016/j.apnum.2005.03.003openalex-snapshot
A fully discrete difference scheme for a diffusion-wave system
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An analysis of the Grünwald–Letnikov scheme for initial-value problems with weakly singular solutions
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Spectral and pseudospectral approximations for the time fractional diffusion equation on an unbounded domain
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Finite difference/spectral approximations for the time-fractional diffusion equation
inferredcites →https://doi.org/10.1016/j.jcp.2014.09.031openalex-snapshot
A new difference scheme for the time fractional diffusion equation
inferredcites →https://doi.org/10.1016/j.jmaa.2011.04.058openalex-snapshot
Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
inferredcites →https://doi.org/10.1016/j.jmaa.2019.03.052openalex-snapshot
Wellposedness and regularity of the variable-order time-fractional diffusion equations
inferredcites →https://doi.org/10.1090/mcom/3304openalex-snapshot
FEM for time-fractional diffusion equations, novel optimal error analyses
inferredcites →https://doi.org/10.1090/mcom/3410openalex-snapshot
Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions
inferredcites →https://doi.org/10.1090/mcom/3413openalex-snapshot
Subdiffusion with a time-dependent coefficient: Analysis and numerical solution
inferredcites →https://doi.org/10.1093/imanum/drt048openalex-snapshot
Well-posedness of hp-version discontinuous Galerkin methods for fractional diffusion wave equations
inferredcites →https://doi.org/10.1093/imanum/drz006openalex-snapshot
A new analysis of a numerical method for the time-fractional Fokker–Planck equation with general forcing
inferredcites →https://doi.org/10.1137/080714130openalex-snapshot
Finite Element Method for the Space and Time Fractional Fokker–Planck Equation
inferredcites →https://doi.org/10.1137/120880719openalex-snapshot
Superconvergence of a Discontinuous Galerkin Method for Fractional Diffusion and Wave Equations
inferredcites →https://doi.org/10.1137/15m1031734openalex-snapshot
Numerical Solution of the Time-Fractional Fokker--Planck Equation with General Forcing
inferredcites →https://doi.org/10.1137/16m1082329openalex-snapshot
Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
inferredcites →https://doi.org/10.1137/16m1175742openalex-snapshot
A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
inferredcites →https://doi.org/10.1137/17m1118816openalex-snapshot
Correction of High-Order BDF Convolution Quadrature for Fractional Evolution Equations
inferredcites →https://doi.org/10.1137/17m1131829openalex-snapshot
Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations
inferredcites →https://doi.org/10.1137/17m1134160openalex-snapshot
Semidiscrete Finite Element Analysis of Time Fractional Parabolic Problems: A Unified Approach
inferredcites →https://doi.org/10.13140/rg.2.2.16993.81766openalex-snapshot
A second-order scheme with nonuniform time steps for a linear reaction-sudiffusion problem
inferredcites →https://doi.org/10.1515/cmam-2017-0019openalex-snapshot
Convergence in Positive Time for a Finite Difference Method Applied to a Fractional Convection-Diffusion Problem
inferredcites →https://doi.org/10.1515/fca-2016-0080openalex-snapshot
Too Much Regularity May Force Too Much Uniqueness
inferredcites →https://doi.org/10.2478/s13540-012-0010-7openalex-snapshot
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Superconvergence Analysis of a Robust Orthogonal Gauss Collocation Method for 2D Fourth-Order Subdiffusion Equations
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Unconditionally Optimal $$H^1$$-Error Analysis of a Two-Grid FEM with $$\alpha $$-Robustness for Nonlinear Time-Fractional Schrödinger Equation with a Weak Initial Singularity
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Uniform stability for a spatially discrete, subdiffusive Fokker–Planck equation
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Sharp error estimate of a Grünwald–Letnikov scheme for reaction-subdiffusion equations
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Unconditional optimal error bounds of the fast nonuniform Alikhanov scheme for a nonlinear time-fractional biharmonic equation
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