On nonnegativity preservation in finite element methods for subdiffusion equations

DOI10.1090/mcom/3167zbMath1364.65197arXiv1510.02825OpenAlexW2343137341MaRDI QIDQ2981776

Vidar Thomée, Bangti Jin, Raytcho D. Lazarov, Zhi Zhou

Publication date: 10 May 2017

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.02825

zbMATH Keywords

Galerkin methodheat equationfinite element methodnumerical experimentssemidiscretefinite volume element methodfractional diffusion equationsCaputo fractional derivativesubdiffusionfully discretemaximum-principlelumped mass methodnonnegativity preservation

Mathematics Subject Classification ID

Heat equation (35K05) Maximum principles in context of PDEs (35B50) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Fractional partial differential equations (35R11) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items (13)

Stability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equations ⋮ A unified Petrov-Galerkin spectral method and fast solver for distributed-order partial differential equations ⋮ Simple positivity-preserving nonlinear finite volume scheme for subdiffusion equations on general non-conforming distorted meshes ⋮ Fully spectral‐Galerkin method for the one‐ and two‐dimensional fourth‐order time‐fractional partial integro‐differential equations with a weakly singular kernel ⋮ Long-time behavior of numerical solutions to nonlinear fractional ODEs ⋮ Asymptotic behavior of solutions to time fractional neutral functional differential equations ⋮ A positivity-preserving and robust fast solver for time-fractional convection-diffusion problems ⋮ Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions ⋮ Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview ⋮ Backward difference formulae: the energy technique for subdiffusion equation ⋮ On positivity preservation in nonlinear finite volume method for multi-term fractional subdiffusion equation on polygonal meshes ⋮ Numerical analysis of backward subdiffusion problems ⋮ Dissipativity and Contractivity Analysis for Fractional Functional Differential Equations and their Numerical Approximations

Uses Software

• Triangle
• DistMesh

Cites Work

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