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We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used…
We consider singularly perturbed convection-diffusion equations on one-dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling condition at inner vertices are…
In this paper, we describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads. On individual roads, we consider the standard Lighthill-Whitham-Richards model which is discretized using the…
We consider a class of fixed-charge transportation problems over graphs. We show that this problem is strongly NP-hard, but solvable in pseudo-polynomial time over trees using dynamic programming. We also show that the LP formulation…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
We present an algorithm for the numerical solution of the equations governing combustion in porous inert media. The discretization of the flow problem is performed by the mixed finite element method, the transport problems are discretized…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…
The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…
We give polynomial-time approximation schemes for monotone maximization problems expressible in terms of distances (up to a fixed upper bound) and efficiently solvable in graphs of bounded treewidth. These schemes apply in all fractionally…
In this paper, we study the large--time behavior of a numerical scheme discretizing drift-- diffusion systems for semiconductors. The numerical method is finite volume in space, implicit in time, and the numerical fluxes are a…
Models describing transport and diffusion processes occurring along the edges of a graph and interlinked by its vertices have been recently receiving a considerable attention. In this paper we generalize such models and consider a network…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
We propose a discrete transport equation on graphs which connects distributions on both vertices and edges. We then derive a discrete analogue of the Benamou-Brenier formulation for Wasserstein-$1$ distance on a graph and as a result…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
We present recent finite element numerical results on a model convection-diffusion problem in the singular perturbed case when the convection term dominates the problem. We compare the standard Galerkin discretization using the linear…
In this work we consider algorithms for reconstructing time-varying data into a finite sum of discrete trajectories, alternatively, an off-the-grid sparse-spikes decomposition which is continuous in time. Recent work showed that this…
An explicit numerical scheme is proposed for solving the initial-boundary value problem for the radiative transport equation in a rectangular domain with completely absorbing boundary condition. An upwind finite difference approximation is…
In this paper, we study dynamical optimal transport on a connected graph from the perspective of the Benamou-Brenier formulation, where densities are assigned to vertices and velocities to edges. However, directly using Newton's method on…
We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy…
In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large…