2 citations · 4 across the 7 of their papers we have counts for
7 papers
A Mountain-Pass Algorithm for Nonlocal Problems with Super-quadratic Nonlinearities
Loic Cappanera, Gabriela Jaramillo, Joshua M. Siktar
In this paper we consider a nonlinear equation with a super-quadratic nonlinearity, , and a nonlocal operator, , generated by a spe…
Artificial compressibility method for the incompressible Navier-Stokes equations with variable density
Cappanera Loic, Giordano Salvatore
We introduce a novel artificial compressibility technique to approximate the incompressible Navier-Stokes equations with variable fluid properties such as density and dynamical vis…
The role of boundary constraints in simulating a nonlocal Gray-Scott model
Loic Cappanera, Gabriela Jaramillo
We present a second-order algorithm for approximating solutions to nonlocal diffusive processes in reaction-diffusion equations. The numerical scheme relies on a quadrature method…
Analysis and Simulations of a Nonlocal Gray-Scott Model
Loic Cappanera, Gabriela Jaramillo, Cory Ward
The Gray-Scott model is a set of reaction-diffusion equations that describes chemical systems far from equilibrium. Interest in this model stems from its ability to generate spatio…
Existence and convergence of a discontinuous Galerkin method for the incompressible three-phase flow problem in porous media
Giselle Sosa Jones, Beatrice Riviere, Loic Cappanera
This paper presents and analyzes a discontinuous Galerkin method for the incompressible three-phase flow problem in porous media. We use a first order time extrapolation which allo…
Numerical Methods for a Diffusive Class Nonlocal Operators
Loic Cappanera, Gabriela Jaramillo, Cory Ward
In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, , of diffusive type. I…
Convergence of a finite element method for degenerate two-phase flow in porous media
Girault Vivette, Riviere Beatrice, Cappanera Loic
A finite element method with mass-lumping and flux upwinding, is formulated for solving the immiscible two-phase flow problem in porous media. The method approximates directly the…