Error estimate for indirect spectral approximation of optimal control problem governed by fractional diffusion equation with variable diffusivity coefficient
DOI10.1016/j.apnum.2021.07.021OpenAlexW3191500522MaRDI QIDQ822170
Fangyuan Wang, Xiangcheng Zheng, Zhaojie Zhou
Publication date: 21 September 2021
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.apnum.2021.07.021
optimal controlJacobi polynomialsvariable coefficientfractional diffusion equationindirect spectral method
Optimality conditions for problems involving partial differential equations (49K20) Smoothness and regularity of solutions to PDEs (35B65) Fractional derivatives and integrals (26A33) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Discrete approximations in optimal control (49M25) Fractional partial differential equations (35R11)
Cites Work
- Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
- A fourth-order approximation of fractional derivatives with its applications
- A discrete method to solve fractional optimal control problems
- Numerical simulation for conservative fractional diffusion equations by an expanded mixed formulation
- Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
- A Legendre collocation method for distributed-order fractional optimal control problems
- Mixed-type Galerkin variational principle and numerical simulation for a generalized nonlocal elastic model
- Wellposedness of the two-sided variable coefficient Caputo flux fractional diffusion equation and error estimate of its spectral approximation
- Finite element approximation of optimal control problem governed by space fractional equation
- Finite element approximation of optimal control problems governed by time fractional diffusion equation
- Fourth order finite difference schemes for time-space fractional sub-diffusion equations
- On the formulation and numerical simulation of distributed-order fractional optimal control problems
- Fractional spectral collocation method for optimal control problem governed by space fractional diffusion equation
- A fast finite volume method for conservative space-time fractional diffusion equations discretized on space-time locally refined meshes
- Numerical approximations for the variable coefficient fractional diffusion equations with non-smooth data
- Numerical schemes for solving the time-fractional dual-phase-lagging heat conduction model in a double-layered nanoscale thin film
- Spectral Galerkin approximation of optimal control problem governed by Riesz fractional differential equation
- Investigations on several high-order ADI methods for time-space fractional diffusion equation
- A hybridized discontinuous Galerkin method for 2D fractional convection-diffusion equations
- A superfast-preconditioned iterative method for steady-state space-fractional diffusion equations
- A general formulation and solution scheme for fractional optimal control problems
- A fast gradient projection method for a constrained fractional optimal control
- Wellposedness of Variable-Coefficient Conservative Fractional Elliptic Differential Equations
- A FEM for an Optimal Control Problem of Fractional Powers of Elliptic Operators
- A Legendre–Galerkin Spectral Method for Optimal Control Problems Governed by Elliptic Equations
- Direct and Inverse Approximation Theorems for the p-Version of the Finite Element Method in the Framework of Weighted Besov Spaces. Part I: Approximability of Functions in the Weighted Besov Spaces
- Analysis of a Time-Stepping Scheme for Time Fractional Diffusion Problems with Nonsmooth Data
- Regularity of the solution to 1-D fractional order diffusion equations
- Spectral Optimization Methods for the Time Fractional Diffusion Inverse Problem
- Optimal Regularity and Error Estimates of a Spectral Galerkin Method for Fractional Advection-Diffusion-Reaction Equations
- Existence and Regularity of solutions to 1-D Fractional Order Diffusion Equations
- A Priori Error Estimates for the Optimal Control of the Integral Fractional Laplacian
- High Order Algorithms for the Fractional Substantial Diffusion Equation with Truncated Lévy Flights
- Variational formulation for the stationary fractional advection dispersion equation
- Variational formulation of problems involving fractional order differential operators
- Pointwise-in-time error estimates for an optimal control problem with subdiffusion constraint
- Stochastic models for fractional calculus
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