We propose and analyze discontinuous Galerkin (dG) approximations to 3D− 1D coupled
systems which model diffusion in a 3D domain containing a small inclusion reduced to its 1D …

We study the linear elasticity system under singular forces. We show the existence and
uniqueness of solutions in two frameworks: weighted Sobolev spaces H 1 (ϖ, Ω), where the …

In this work, a numerical solution technique for an elliptic Dirac problem is investigated. One
reason to study this issue is that this partial differential equation (PDE) is closely related to a …

This paper is devoted to a discontinuous Galerkin (DG) method for nonlinear quasistatic
poroelasticity problems. The fully implicit nonlinear numerical scheme is constructed by …

In this work, we examine the discontinuous Galerkin method for parabolic linear problem
with data in L 1 (Ω×(0, T)). On one hand, using a Euler time advancing scheme that goes …

Three dimensional elliptic problems with variable coefficients and line Dirac sources arise in
a number of fields. The lack of regularity on the solution prompts users to turn towards …