
Numerical Analysis of Backward Subdiffusion Problems
The aim of this paper is to develop and analyze numerical schemes for ap...
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Stable Backward Diffusion Models that Minimise Convex Energies
Backward diffusion processes appear naturally in image enhancement and d...
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Numerical Estimation of a Diffusion Coefficient in Subdiffusion
In this work, we consider the numerical recovery of a spatially dependen...
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Identifying source term in the subdiffusion equation with L^2TV regularization
In this paper, we consider the inverse source problem for the timefract...
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Numerical algorithm for the model describing anomalous diffusion in expanding media
We provide a numerical algorithm for the model characterizing anomalous ...
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Asymptotically compatible reproducing kernel collocation and meshfree integration for nonlocal diffusion
Reproducing kernel (RK) approximations are meshfree methods that constru...
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Stability and Functional Superconvergence of NarrowStencil SecondDerivative Generalized SummationByParts Discretizations
We analyze the stability and functional superconvergence of discretizati...
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Backward diffusionwave problem: stability, regularization and approximation
We aim at the development and analysis of the numerical schemes for approximately solving the backward diffusionwave problem, which involves a fractional derivative in time with order α∈(1,2). From terminal observations at two time levels, i.e., u(T_1) and u(T_2), we simultaneously recover two initial data u(0) and u_t(0) and hence the solution u(t) for all t > 0. First of all, existence, uniqueness and Lipschitz stability of the backward diffusionwave problem were established under some conditions about T_1 and T_2. Moreover, for noisy data, we propose a quasiboundary value scheme to regularize the "mildly" illposed problem, and show the convergence of the regularized solution. Next, to numerically solve the regularized problem, a fully discrete scheme is proposed by applying finite element method in space and convolution quadrature in time. We establish error bounds of the discrete solution in both cases of smooth and nonsmooth data. The error estimate is very useful in practice since it indicates the way to choose discretization parameters and regularization parameter, according to the noise level. The theoretical results are supported by numerical experiments.
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