The time-fractional diffusion inverse problem subject to an extra measurement by a local discontinuous Galerkin method

DOI10.1007/s10543-018-0731-zzbMath1420.65097OpenAlexW2894679878MaRDI QIDQ1731611

Nazdar Abdollahi, Davood Rostamy, Samaneh Qasemi

Publication date: 13 March 2019

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-018-0731-z

zbMATH Keywords

existenceinverse problemuniquenesserror estimateRiemann-Liouville derivativelocal discontinuous Galerkin method

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical quadrature and cubature formulas (65D32) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Fractional partial differential equations (35R11)

Related Items

MLPG method based on particular solution to identify a time-dependent boundary source for the time-fractional diffusion equation ⋮ An inverse random source problem for the time-space fractional diffusion equation driven by fractional Brownian motion ⋮ Reconstruction of the time-dependent source term in a stochastic fractional diffusion equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An inverse problem for a generalized fractional diffusion
• The local discontinuous Galerkin finite element method for Burger's equation
• On the uniqueness and reconstruction for an inverse problem of the fractional diffusion process
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• A class of nonlinear non-classical parabolic equations
• Fractional vector calculus and fractional Maxwell's equations
• Particle tracking for fractional diffusion with two time scales
• Implicit finite difference approximation for time fractional diffusion equations
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• An algorithm for the numerical solution of differential equations of fractional order
• Discontinuous Galerkin method for an integro-differential equation modeling dynamic fractional order viscoelasticity
• Inverse source problem for a time-fractional diffusion equation with nonlocal boundary conditions
• Existence and uniqueness of an inverse source problem for a fractional integrodifferential equation
• Time fractional IHCP with Caputo fractional derivatives
• Space-dependent source determination in a time-fractional diffusion equation using a local discontinuous Galerkin method
• A modified quasi-boundary value method for an inverse source problem of the time-fractional diffusion equation
• Solving an inverse parabolic problem by optimization from final measurement data
• Maximum principle for the generalized time-fractional diffusion equation
• Reconstruction of a time-dependent source term in a time-fractional diffusion equation
• Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
• The Maximum Principle for Time-Fractional Diffusion Equations and Its Application
• An inverse time-dependent source problem for a time-fractional diffusion equation
• Inverse problem for fractional diffusion equation
• An inverse problem for a one-dimensional time-fractional diffusion problem
• Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications
• Asymptotic Error Expansions for the Finite Element Method for Second Order Elliptic Problems in $R^N$, $N\geq2$. I: Local Interior Expansions
• A posteriori error estimates in a globally convergent FEM for a hyperbolic coefficient inverse problem
• Inverse source problem for a fractional diffusion equation
• Robin coefficient identification for a time-fractional diffusion equation
• Discontinuous Petrov-Galerkin and Bernstein-Legendre Polynomials Method for Solving Fractional Damped Heat- and Wave-like Equations
• A Local Discontinuous Galerkin Method for the Camassa–Holm Equation
• An inverse source problem for a one-dimensional space–time fractional diffusion equation
• Fractional Partial Differential Equations and Their Numerical Solutions
• The new streamline diffusion for the 3D coupled Schrodinger equations with a cross-phase modulation
• Numerical solutions of some parabolic inverse problems
• Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation
• A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• Gegenbauer Cardinal Functions for the Inverse Source Parabolic Problem with a Time-Fractional Diffusion Equation
• Existence and Uniqueness of the Weak Solution of the Space-time Fractional Diffusion Equation and a Spectral Method Approximation
• Local Discontinuous Galerkin methods for fractional diffusion equations
• A backward problem for the time-fractional diffusion equation
• The random walk's guide to anomalous diffusion: A fractional dynamics approach