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Due to their wide appearance in environmental settings as well as industrial and medical applications, the Stokes-Darcy problems with different sets of interface conditions establish an active research area in the community of mathematical…
We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
In \cite{CJ1} M. Jaoua et al. studied the linear approximation of Robin problem on $\Omega$ an open bounded domain of $\R^d$, and they given some important results. In this paper, we study a nonlinear approximation of an elliptic problem…
This work is a continuation of [E. Bonnetier, D.Bresch, V. Milisic, submitted]; it deals with rough boundaries in the simplified context of a Poisson equation. We impose Dirichlet boundary conditions on the periodic microscopic perturbation…
Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries…
This paper presents an efficient high-order sharp-interface method for solving the three-dimensional (3D) Poisson equation with Dirichlet boundary conditions on a nonuniform Cartesian grid with irregular domain boundaries. The new approach…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
We consider joint inversion for two or more unknown parameters from observational data in the Bayesian framework. Standard approaches often either treat the parameters as independent or impose structural similarity through regularisation…
We investigate the realization of a myriad of general local and nonlocal inhomogeneous elliptic and parabolic boundary value problems over classes of irregular regions. We present a unified approach in which either local or nonlocal…
Parabolic equations on evolving domains model a multitude of applications including various industrial processes such as the molding of heated materials. Such equations are numerically challenging as they require large-scale computations…
In this paper, we consider the inverse problem of detecting a corrosion coefficient between two layers of a conducting medium from the Neumann-to-Dirichlet map. This inverse problem is motivated by the description of the index of corrosion…
We prove convergence for the nonoverlapping Robin-Robin method applied to nonlinear elliptic equations with a $p$-structure, including degenerate diffusion equations governed by the $p$-Laplacian. This nonoverlapping domain decomposition is…
We revise the Bayesian inference steps required to analyse the cosmological large-scale structure. Here we make special emphasis in the complications which arise due to the non-Gaussian character of the galaxy and matter distribution. In…
Reliable tracking of moving boundaries is important for the simulation of compressible fluid flows and there are a lot of contributions in literature. We recognize from the classical piston problem, a typical moving boundary problem in gas…
In unconstrained maximum a posteriori (MAP) and maximum likelihood estimation, the inverse of minus the merit-function Hessian matrix is an approximation of the estimate covariance matrix. In the Bayesian context of MAP estimation, it is…
Research on smooth vector graphics is separated into two independent research threads: one on interpolation-based gradient meshes and the other on diffusion-based curve formulations. With this paper, we propose a mathematical formulation…
In a Cox model, the partial likelihood, as the product of a series of conditional probabilities, is used to estimate the regression coefficients. In practice, those conditional probabilities are approximated by risk score ratios based on a…
It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated…
This paper aims to combine the advantages of the Jordan-Moore-Gibson-Thompson JMGT equation as an advanced model in nonlinear acoustics with a frequency domain formulation of the forward and inverse problem of acoustic nonlinearity…
This paper presents a new approach for Gaussian process (GP) regression for large datasets. The approach involves partitioning the regression input domain into multiple local regions with a different local GP model fitted in each region.…