Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data

From MaRDI portal
Publication:3464421

DOI10.1137/140979563zbMath1381.65082arXiv1404.3800OpenAlexW2274070693MaRDI QIDQ3464421

Zhi Zhou, Bangti Jin, Raytcho D. Lazarov

Publication date: 27 January 2016

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.3800




Related Items

A block-centred finite difference method for the distributed-order differential equation with Neumann boundary conditionAnalysis of Legendre pseudospectral approximations for nonlinear time fractional diffusion-wave equationsNumerical discretization and fast approximation of a variably distributed-order fractional wave equationA Survey of the L1 Scheme in the Discretisation of Time-Fractional ProblemsBackward Diffusion-Wave Problem: Stability, Regularization, and ApproximationA generalized quasi-boundary value method for recovering a source in a fractional diffusion-wave equationA compact ADI scheme for the two dimensional time fractional diffusion-wave equation in polar coordinatesTime Discretization of a Tempered Fractional Feynman--Kac Equation with Measure DataNumerical analysis of multi-term time-fractional nonlinear subdiffusion equations with time delay: what could possibly go wrong?Semidiscrete Finite Element Analysis of Time Fractional Parabolic Problems: A Unified ApproachA single-step correction scheme of Crank-Nicolson convolution quadrature for the subdiffusion equationTwo-grid methods for nonlinear time fractional diffusion equations by \(L 1\)-Galerkin FEMAnalysis of a Fully Discrete Finite Element Method for Parabolic Interface Problems with Nonsmooth Initial DataStrong Convergence Order for the Scheme of Fractional Diffusion Equation Driven by Fractional Gaussian NoiseFinite Difference Method for Inhomogeneous Fractional Dirichlet ProblemError Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion EquationMultigrid Waveform Relaxation for the Time-Fractional Heat EquationA symmetric fractional-order reduction method for direct nonuniform approximations of semilinear diffusion-wave equationsA Crank-Nicolson-type compact difference method and its extrapolation for time fractional Cattaneo convection-diffusion equations with smooth solutionsError estimate on the tanh meshes for the time fractional diffusion equationA nonuniform L2 formula of Caputo derivative and its application to a fractional Benjamin–Bona–Mahony‐type equation with nonsmooth solutionsSharp error estimates for spatial-temporal finite difference approximations to fractional sub-diffusion equation without regularity assumption on the exact solution\({\boldsymbol{H^1}}\) -Norm Stability and Convergence of an L2-Type Method on Nonuniform Meshes for Subdiffusion EquationA second-order finite difference scheme for the multi-dimensional nonlinear time-fractional Schrödinger equationNumerical approximations for the nonlinear time fractional reaction–diffusion equationA Cα finite difference method for the Caputo time‐fractional diffusion equationError Analysis for a Fractional-Derivative Parabolic Problem on Quasi-Graded Meshes using Barrier FunctionsA linear Galerkin numerical method for a quasilinear subdiffusion equationError analysis of a finite difference scheme on a modified graded mesh for a time-fractional diffusion equationNumerical methods for fractional diffusionA Spectrally Accurate Approximation to Subdiffusion Equations Using the Log Orthogonal FunctionsUnnamed ItemSecond-order difference approximations for Volterra equations with the completely monotonic kernelsNumerical solutions of fourth‐order fractional sub‐diffusion problems via parametric quintic splineA finite-difference scheme on a graded mesh for solving Cauchy problems with a fractional Caputo derivative in a Banach spaceThe compact difference scheme for the fourth‐order nonlocal evolution equation with a weakly singular kernelA Sharp $\alpha$-Robust $L1$ Scheme on Graded Meshes for Two-Dimensional Time Tempered Fractional Fokker-Planck EquationUnconditionally Convergent $L1$-Galerkin FEMs for Nonlinear Time-Fractional Schrödinger EquationsLocal error estimates of the fourth-order compact difference scheme for a time-fractional diffusion-wave equationCorrection of High-Order BDF Convolution Quadrature for Fractional Evolution EquationsNumerical solution to a linearized time fractional KdV equation on unbounded domainsNumerical Analysis of Nonlinear Subdiffusion EquationsAn Analysis of the Modified L1 Scheme for Time-Fractional Partial Differential Equations with Nonsmooth DataDiscrete approximation of solutions of the Cauchy problem for a linear homogeneous differential-operator equation with a Caputo fractional derivative in a Banach spaceA fully discrete scheme based on cubic splines and its analysis for time-fractional reaction-diffusion equations exhibiting weak initial singularityA higher order numerical scheme for solving fractional Bagley‐Torvik equationUnconditionally stable and convergent difference scheme for superdiffusion with extrapolationGalerkin Finite Element Approximations for Stochastic Space-Time Fractional Wave EquationsGeneralized Jacobi Spectral Galerkin Method for Fractional-Order Volterra Integro-Differential Equations with Weakly Singular KernelsA Kernel Compression Scheme for Fractional Differential EquationsL1 scheme for solving an inverse problem subject to a fractional diffusion equationA high-order adaptive numerical algorithm for fractional diffusion wave equation on non-uniform meshesOn nonnegativity preservation in finite element methods for subdiffusion equationsError analysis of an L2-type method on graded meshes for a fractional-order parabolic problemError analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensionsSubdiffusion with a time-dependent coefficient: Analysis and numerical solutionHigh-order Time Stepping Schemes for Semilinear Subdiffusion EquationsSharp convergence rates of time discretization for stochastic time-fractional PDEs subject to additive space-time white noiseA Second Order Time Accurate Finite Volume Scheme for the Time-Fractional Diffusion Wave Equation on General Nonconforming MeshesAnalysis of a Time-Stepping Scheme for Time Fractional Diffusion Problems with Nonsmooth DataAn inverse potential problem for subdiffusion: stability and reconstruction*Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion EquationsAnalysis of L1-Galerkin FEMs for Time-Fractional Nonlinear Parabolic ProblemsA Parallel-in-Time Algorithm for High-Order BDF Methods for Diffusion and Subdiffusion EquationsAlgebraic Conditions for Stability Analysis of Linear Time‐Invariant Distributed Order Dynamic Systems: A Lagrange Inversion Theorem ApproachRecovering the potential and order in one-dimensional time-fractional diffusion with unknown initial condition and source *Numerical approximations for a fully fractional Allen–Cahn equationError analysis of a FVEM for fractional order evolution equations with nonsmooth initial dataNumerical Approximation of Semilinear Subdiffusion Equations with Nonsmooth Initial DataReconstruction of a time-dependent source term in a time-fractional diffusion-wave equationNumerical algorithm for the model describing anomalous diffusion in expanding mediaNumerical approximation of stochastic time-fractional diffusionError estimates for a robust finite element method of two-term time-fractional diffusion-wave equation with nonsmooth dataWell-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable orderNumerical Estimation of a Diffusion Coefficient in SubdiffusionStability and Convergence Analyses of the FDM Based on Some L-Type Formulae for Solving the Subdiffusion EquationStability and numerical analysis of backward problem for subdiffusion with time-dependent coefficientsNumerical methods for fractional partial differential equationsNumerical solution of time-fractional fourth-order reaction-diffusion model arising in composite environmentsConvergence and superconvergence analyses of HDG methods for time fractional diffusion problemsEfficient Galerkin finite element methods for a time-fractional Cattaneo equationFinite element approximation of time fractional optimal control problem with integral state constraintFractional time stepping and adjoint based gradient computation in an inverse problem for a fractionally damped wave equationTwo-grid finite element methods for nonlinear time-fractional parabolic equationsFinite difference/spectral approximations for the distributed order time fractional reaction-diffusion equation on an unbounded domainRecovery of advection coefficient and fractional order in a time-fractional reaction-advection-diffusion-wave equationNumerical schemes for the time-fractional mobile/immobile transport equation based on convolution quadratureA novel discrete fractional Grönwall-type inequality and its application in pointwise-in-time error estimates\(\alpha\)-robust \(H^1\)-norm analysis of a finite element method for the superdiffusion equation with weak singularity solutionsAnalysis of a full discretization for a fractional/normal diffusion equation with rough Dirichlet boundary dataA linearized second-order scheme for nonlinear time fractional Klein-Gordon type equationsAnalysis of stability and convergence for L-type formulas combined with a spatial finite element method for solving subdiffusion problemsThe lumped mass FEM for a time-fractional cable equationAnalysis of two methods based on Galerkin weak form for fractional diffusion-wave: meshless interpolating element free Galerkin (IEFG) and finite element methodsTwo time-stepping schemes for sub-diffusion equations with singular source termsNonsmooth data error estimates for FEM approximations of the time fractional cable equationA fitted scheme for a Caputo initial-boundary value problemUnconditional convergence in maximum-norm of a second-order linearized scheme for a time-fractional Burgers-type equationStability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equationsA unified numerical scheme for the multi-term time fractional diffusion and diffusion-wave equations with variable coefficientsNumerical reconstruction of the spatial component in the source term of a time-fractional diffusion equationPreprocessing schemes for fractional-derivative problems to improve their convergence ratesAsymptotically compatible schemes for space-time nonlocal diffusion equationsAn approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth dataGalerkin type methods for semilinear time-fractional diffusion problemsNumerical scheme for the Fokker-Planck equations describing anomalous diffusions with two internal statesHigher order time stepping methods for subdiffusion problems based on weighted and shifted Grünwald-Letnikov formulae with nonsmooth dataDiscrete maximal regularity of time-stepping schemes for fractional evolution equationsSubdiffusion with time-dependent coefficients: improved regularity and second-order time steppingSecond-order stable finite difference schemes for the time-fractional diffusion-wave equationFinite element error analysis of a time-fractional nonlocal diffusion equation with the Dirichlet energySpace-time Petrov-Galerkin FEM for fractional diffusion problemsTime discretization of fractional subdiffusion equations via fractional resolvent operatorsHigh-order numerical methods for solving time fractional partial differential equationsIsogeometric analysis for time-fractional partial differential equationsA space-time finite element method for fractional wave problemsA novel discrete Gronwall inequality in the analysis of difference schemes for time-fractional multi-delayed diffusion equationsNumerical algorithm for the space-time fractional Fokker-Planck system with two internal statesCorrection of high-order BDF convolution quadrature for fractional Feynman-Kac equation with Lévy flightError estimates of high-order numerical methods for solving time fractional partial differential equationsAnalysis of a temporal discretization for a semilinear fractional diffusion equationNumerical analysis of two Galerkin discretizations with graded temporal grids for fractional evolution equationsTime-fractional Allen-Cahn equations: analysis and numerical methodsIterative methods for mesh approximations of optimal control problems controlled by linear equations with fractional derivativesHigh-order BDF fully discrete scheme for backward fractional Feynman-Kac equation with nonsmooth dataComputational inverse problems for partial differential equations. Abstracts from the workshop held December 6--12, 2020 (hybrid meeting)Convergence of finite element solutions of stochastic partial integro-differential equations driven by white noiseFourth-order compact difference schemes for the two-dimensional nonlinear fractional mobile/immobile transport modelsA graded scheme with bounded grading for a time-fractional Boussinesq type equationToo much regularity may force too much uniquenessFinite difference approximation of fractional wave equation with concentrated capacityNumerical methods for time-fractional evolution equations with nonsmooth data: a concise overviewNotes on the convergence order of gradient schemes for time fractional differential equationsAnalysis and discretization of a variable-order fractional wave equationCompact finite difference schemes for the time fractional diffusion equation with nonlocal boundary conditionsFinite element method for fractional parabolic integro-differential equations with smooth and nonsmooth initial dataAnalysis of a nonlocal-in-time parabolic equationA high-order compact difference method on fitted meshes for Neumann problems of time-fractional reaction-diffusion equations with variable coefficientsA Gauss-Jacobi kernel compression scheme for fractional differential equationsVariational formulation of time-fractional parabolic equationsA new analysis for the convergence of the gradient discretization method for multidimensional time fractional diffusion and diffusion-wave equationsFinite difference/finite element method for a nonlinear time-fractional fourth-order reaction-diffusion problemSuperconvergence error estimate of a finite element method on nonuniform time meshes for reaction-subdiffusion equationsGalerkin spectral method for nonlinear time fractional cable equation with smooth and nonsmooth solutionsAnalysis of the L1 scheme for fractional wave equations with nonsmooth dataFast algorithms for convolution quadrature of Riemann-Liouville fractional derivativeThe unique identification of variable-order fractional wave equationsA class of efficient time-stepping methods for multi-term time-fractional reaction-diffusion-wave equationsFast high-order difference scheme for the modified anomalous subdiffusion equation based on fast discrete sine transformBernstein dual-Petrov-Galerkin method: application to 2D time fractional diffusion equationBackward difference formulae: the energy technique for subdiffusion equationTemporally semidiscrete approximation of a Dirichlet boundary control for a fractional/normal evolution equation with a final observationA-posteriori error estimations based on postprocessing technique for two-sided fractional differential equationsSeveral effective algorithms for nonlinear time fractional modelsOn positivity preservation in nonlinear finite volume method for multi-term fractional subdiffusion equation on polygonal meshesA high-order compact finite difference method on nonuniform time meshes for variable coefficient reaction-subdiffusion problems with a weak initial singularityMultigrid methods for time-fractional evolution equations: a numerical studyA high-order scheme for fractional ordinary differential equations with the Caputo-Fabrizio derivativeTwo \(L1\) schemes on graded meshes for fractional Feynman-Kac equationA fast linearized finite difference method for the nonlinear multi-term time-fractional wave equationAn improved finite difference/finite element method for the fractional Rayleigh-Stokes problem with a nonlinear source termPreface: Numerical analysis of fractional differential equationsNumerical approximation of space-time fractional parabolic equationsA Crank-Nicolson-type compact difference method with the uniform time step for a class of weakly singular parabolic integro-differential equationsExplicit representation of discrete fractional resolvent families in Banach spacesDetermining a time-dependent coefficient in a time-fractional diffusion-wave equation with the Caputo derivative by an additional integral conditionConvergence analysis of a Petrov-Galerkin method for fractional wave problems with nonsmooth dataSpectral approximations for nonlinear fractional delay diffusion equations with smooth and nonsmooth solutionsIncomplete iterative solution of subdiffusionFinite element approximations for fractional evolution problemsA high-order method with a temporal nonuniform mesh for a time-fractional Benjamin-Bona-Mahony equationFinite element methods based on two families of second-order numerical formulas for the fractional cable model with smooth solutionsError estimates for backward fractional Feynman-Kac equation with non-smooth initial dataNumerical algorithms of the two-dimensional Feynman-Kac equation for reaction and diffusion processesAn efficient space-time method for time fractional diffusion equationConvergence and stability of compact finite difference method for nonlinear time fractional reaction-diffusion equations with delayError of the Galerkin scheme for a semilinear subdiffusion equation with time-dependent coefficients and nonsmooth dataDiscontinuous Galerkin method for a distributed optimal control problem governed by a time fractional diffusion equation



Cites Work


This page was built for publication: Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data