Related papers: Numerical solution of the boundary value problem o…
Applied problems of oil and gas recovery are studied numerically using the mathematical models of multiphase fluid flows in porous media. The basic model includes the continuity equations and the Darcy laws for each phase, as well as the…
We study an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes using the CutFEM method. Our main contribution is the reconstruction of conservative fluxes from the CutFEM solution and their use in a…
In this paper, we proposed two new types of edge multiscale methods motivated by \cite{GL18} to solve Partial Differential Equations (PDEs) with high-contrast heterogeneous coefficients: Edge spectral multiscale Finte Element method…
We develop a new computational framework to solve the partial differential equations (PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time stochastic nonlinear systems. The need for computing the…
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…
In this paper we develop an $hp$-adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbation. Our approach combines both adaptive Newton schemes and…
To numerically solve the two-dimensional advection equation, we propose a family of fourth- and higher-order semi-Lagrangian finite volume (SLFV) methods that feature (1) fourth-, sixth-, and eighth-order convergence rates, (2)…
We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…
We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible…
A hybrid computational approach that integrates the finite element method (FEM) with least squares support vector regression (LSSVR) is introduced to solve partial differential equations. The method combines FEM's ability to provide the…
In this paper, authors focus effort on improving the conventional discrete velocity method (DVM) into a multiscale scheme in finite volume framework for gas flow in all flow regimes. Unlike the typical multiscale kinetic methods unified…
Thermal decay rate over an edge-shaped barrier at high dissipation is studied numerically through the computer modeling. Two sorts of the stochastic Langevin type equations are applied: (i) the Langevin equations for the coordinate and…
We introduce a new algorithm to solve a regularized spatial-spectral image estimation problem. Our approach is based on the linearized alternating directions method of multipliers (LADMM), which is a variation of the popular ADMM algorithm.…
We construct an efficient numerical scheme for solving obstacle problems in divergence form. The numerical method is based on a reformulation of the obstacle in terms of an L1-like penalty on the variational problem. The reformulation is an…
A common strategy in the numerical solution of partial differential equations is to define a uniform discretization of a tensor-product multi-dimensional logical domain, which is mapped to a physical domain through a given coordinate…
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
The diffuse domain method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental issues in the analysis are still widely open. In this paper we…
Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…
We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the…
We develop, and implement in a Finite Volume environment, a density-based approach for the Euler equations written in conservative form using density, momentum, and total energy as variables. Under simplifying assumptions, these equations…