Let be a convex polytope (). The Ritz projection is the best approximation, in the-norm, to a
given function in a finite element space. When such finite element spaces are constructed on …

In Lipschitz domains, we study a Darcy–Forchheimer problem coupled with a singular heat
equation by a nonlinear forcing term depending on the temperature. By singular we mean …

The analyses of interior penalty discontinuous Galerkin methods of any order k for solving
elliptic and parabolic problems with Dirac line sources are presented. For the steady state …

We show that on convex polytopes in two or three dimensions, the finite element Stokes
projection is stable on weighted spaces ${\mathbf {W}}^{1, p} _0 (\omega,\Omega)\times L …

We show the well posedness of the Poisson and Stokes problems on weighted spaces over
general Lipschitz domains. For a particular range of p, we consider those weights in the …

We study the Stokes problem over convex polyhedral domains on weighted Sobolev
spaces. The weight is assumed to belong to the Muckenhoupt class A q for q∈(1,∞). We …

In two dimensions, we propose and analyze an a posteriori error estimator for finite element
approximations of the stationary Navier--Stokes equations with singular sources on …

Starting from full-dimensional models of solute transport, we derive and analyze multi-
dimensional models of time-dependent convection, diffusion, and exchange in and around …

When solving elliptic partial differential equations in a region containing immersed interfaces
(possibly evolving in time), it is often desirable to approximate the problem using an …

In Lipschitz two-and three-dimensional domains, we study the existence for the so-called
Boussinesq model of thermally driven convection under singular forcing. By singular we …