Related papers: Numerical Reconstruction and Analysis of Backward …
We consider the multidimensional space-fractional diffusion equations with spatially varying diffusivity and fractional order. Significant computational challenges are encountered when solving these equations due both to the kernel…
We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to be unconditionally stable by choosing suitable parameters.…
The numerical solution of a nonlinear and space-fractional anti-diffusive equation used to model dune morphodynamics is considered. Spatial discretization is effected using a finite element method whereas the Crank-Nicolson scheme is used…
We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…
In this work, we study an inverse problem of recovering a space-time dependent diffusion coefficient in the subdiffusion model from the distributed observation, where the mathematical model involves a Djrbashian-Caputo fractional derivative…
This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…
Building on the well-known total-variation (TV), this paper develops a general regularization technique based on nonlinear isotropic diffusion (NID) for inverse problems with piecewise smooth solutions. The novelty of our approach is to be…
Inverse problems generally require a regularizer or prior for a good solution. A recent trend is to train a convolutional net to denoise images, and use this net as a prior when solving the inverse problem. Several proposals depend on a…
This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…
This paper deals with the construction of numerical stable solutions of random mean square Fisher-KPP models with advection. The construction of the numerical scheme is performed in two stages. Firstly, a semidiscretization technique…
This paper investigates the stability of both the semi-discrete and the implicit central scheme for the linear damped wave equation on the half-line, where the spatial boundary is characteristic for the limiting equation. The proposed…
We present a fully discrete finite element method for the interior null controllability problem subject to the wave equation. For the numerical scheme, piece-wise affine continuous elements in space and finite differences in time are…
A critical challenge inherent to the projection method applied to the Landau-Lifshitz equation is the deficiency of rigorous theoretical justifications for the stability of its projection step. To mitigate this limitation, we introduce a…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
We develop an efficient numerical scheme for the 3D mean-field spherical dynamo equation. The scheme is based on a semi-implicit discretization in time and a spectral method in space based on the divergence-free spherical harmonic…
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…
We couple the L1 discretization of the Caputo fractional derivative in time with the Galerkin scheme to devise a linear numerical method for the semilinear subdiffusion equation. Two important points that we make are: nonsmooth initial data…
Convergence results are shown for full discretizations of quasilinear parabolic partial differential equations on evolving surfaces. As a semidiscretization in space the evolving surface finite element method is considered, using a…
We introduce a novel formulation for curvature regularization by penalizing normal curvatures from multiple directions. This total normal curvature regularization is capable of producing solutions with sharp edges and precise isotropic…
Stability and convergence of full discretizations of various surface evolution equations are studied in this paper. The proposed discretization combines a higher-order evolving-surface finite element method (ESFEM) for space discretization…