Error estimates for approximations of distributed order time fractional diffusion with nonsmooth data

DOI10.1515/fca-2016-0005zbMath1333.65111arXiv1504.01529OpenAlexW2963020731MaRDI QIDQ261251

Bangti Jin, Dongwoo Sheen, Raytcho D. Lazarov, Zhi Zhou

Publication date: 23 March 2016

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.01529

zbMATH Keywords

error estimatesGalerkin finite element methodfully discrete schemedistributed orderfractional diffusion

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11)

Related Items

Numerical approach for a class of distributed order time fractional partial differential equations ⋮ The well-posedness analysis of distributed order fractional diffusion problems on \(\mathbb{R}^N\) ⋮ Finite difference/finite element methods for distributed-order time fractional diffusion equations ⋮ Efficient alternating direction implicit numerical approaches for multi-dimensional distributed-order fractional integro differential problems ⋮ Stability analysis of linear distributed order fractional systems with distributed delays ⋮ A numerical method for solving the time fractional Schrödinger equation ⋮ Stability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equations ⋮ Backward problem for a time-space fractional diffusion equation ⋮ A unified Petrov-Galerkin spectral method and fast solver for distributed-order partial differential equations ⋮ An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data ⋮ A fast Alikhanov algorithm with general nonuniform time steps for a two‐dimensional distributed‐order time–space fractional advection–dispersion equation ⋮ A fully discrete LDG method for the distributed-order time-fractional reaction-diffusion equation ⋮ High-order orthogonal spline collocation ADI scheme for a new complex two-dimensional distributed-order fractional integro-differential equation with two weakly singular kernels ⋮ Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space distributed-order diffusion equation ⋮ An ADI orthogonal spline collocation method for a new two-dimensional distributed-order fractional integro-differential equation ⋮ Solving a backward problem for a distributed-order time fractional diffusion equation by a new adjoint technique ⋮ The well-posedness for the distributed-order wave equation on \(\mathbb{R}^N\) ⋮ A second-order difference scheme for generalized time-fractional diffusion equation with smooth solutions ⋮ Equivalence of definitions of solutions for some class of fractional diffusion equations ⋮ High spatial accuracy analysis of linear triangular finite element for distributed order diffusion equations ⋮ Error estimates of high-order numerical methods for solving time fractional partial differential equations ⋮ An alternating direction implicit Galerkin finite element method for the distributed-order time-fractional mobile-immobile equation in two dimensions ⋮ On nonnegativity preservation in finite element methods for subdiffusion equations ⋮ Arbitrarily High-Order Exponential Cut-Off Methods for Preserving Maximum Principle of Parabolic Equations ⋮ The Crank-Nicolson type compact difference schemes for a loaded time-fractional Hallaire equation ⋮ A backward problem for distributed order diffusion equation: uniqueness and numerical solution ⋮ Numerical solution for diffusion equations with distributed order in time using a Chebyshev collocation method ⋮ TT-M FE method for a 2D nonlinear time distributed-order and space fractional diffusion equation ⋮ Efficient solution of time-fractional differential equations with a new adaptive multi-term discretization of the generalized Caputo-Dzherbashyan derivative ⋮ Algebraic Conditions for Stability Analysis of Linear Time‐Invariant Distributed Order Dynamic Systems: A Lagrange Inversion Theorem Approach ⋮ WSGD-OSC scheme for two-dimensional distributed order fractional reaction-diffusion equation ⋮ Approximation methods for the distributed order calculus using the convolution quadrature ⋮ On positivity preservation in nonlinear finite volume method for multi-term fractional subdiffusion equation on polygonal meshes ⋮ An RBF based meshless method for the distributed order time fractional advection-diffusion equation ⋮ Two implicit meshless finite point schemes for the two-dimensional distributed-order fractional equation ⋮ Устойчивость и сходимость разностных схем для уравнения диффузии дискретно-распределенного порядка с обобщенными функциями памяти ⋮ Space-time finite element method for the distributed-order time fractional reaction diffusion equations ⋮ A time-fractional diffusion equation with generalized memory kernel in differential and difference settings with smooth solutions ⋮ Analysis and fast approximation of a steady-state spatially-dependent distributed-order space-fractional diffusion equation ⋮ Explicit representation of discrete fractional resolvent families in Banach spaces ⋮ Analysis of a hidden memory variably distributed-order space-fractional diffusion equation ⋮ Fast high-order compact difference scheme for the nonlinear distributed-order fractional Sobolev model appearing in porous media ⋮ Numerical methods for fractional partial differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical solution of distributed order fractional differential equations
• Numerical approximation of distributed order reaction-diffusion equations
• An analysis of the Rayleigh-Stokes problem for a generalized second-grade fluid
• The Galerkin finite element method for a multi-term time-fractional diffusion equation
• An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time
• Numerical solution via Laplace transforms of a fractional order evolution equation
• Numerical analysis for distributed-order differential equations
• Convolution quadrature and discretized operational calculus. I
• Continuous time random walk models associated with distributed order diffusion equations
• Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations
• Some high-order difference schemes for the distributed-order differential equations
• Distributed order calculus and equations of ultraslow diffusion
• The functional calculus for sectorial operators
• Stochastic model for ultraslow diffusion
• An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data
• Time-fractional Diffusion of Distributed Order
• Natural and Modified Forms of Distributed-Order Fractional Diffusion Equations
• Convolution quadrature time discretization of fractional diffusion-wave equations
• Parabolic and hyperbolic contours for computing the Bromwich integral
• A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature
• A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature
• Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term
• Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations
• A tutorial on inverse problems for anomalous diffusion processes
• Completely monotone functions and some classes of fractional evolution equations
• Galerkin Finite Element Methods for Parabolic Problems