Finite Element Discretizations of a Convective Brinkman–Forchheimer Model Under Singular Forcing

A Allendes, G Campaña, E Otárola - Journal of Scientific Computing, 2024 - Springer
In two-dimensional bounded Lipschitz domains, we analyze a convective Brinkman–
Forchheimer problem on the weighted spaces H 0 1 (ω, Ω)× L 2 (ω, Ω)/R, where ω belongs …

Parabolic Lipschitz truncation and caloric approximation

L Diening, S Schwarzacher, B Stroffolini… - Calculus of Variations and …, 2017 - Springer
We develop an improved version of the parabolic Lipschitz truncation, which allows
qualitative control of the distributional time derivative and the preservation of zero boundary …

A posteriori error estimates for the Stokes problem with singular sources

A Allendes, E Otárola, AJ Salgado - Computer Methods in Applied …, 2019 - Elsevier
We propose a posteriori error estimators for classical low-order inf–sup stable and stabilized
finite element approximations of the Stokes problem with singular sources in two and three …

Stability of the Stokes projection on weighted spaces and applications

R Durán, E Otárola, A Salgado - Mathematics of Computation, 2020 - ams.org
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 …

The Poisson and Stokes problems on weighted spaces in Lipschitz domains and under singular forcing

E Otárola, AJ Salgado - Journal of Mathematical Analysis and Applications, 2019 - Elsevier
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 …

Regularity estimates for stationary Stokes problem in some generalized function spaces

TN Nguyen, MP Tran, NTN Tran - Zeitschrift für angewandte Mathematik …, 2023 - Springer
We investigate the global regularity for weak solutions to a generalized stationary Stokes
problem with BMO coefficients in a non-smooth domains. The results in this paper fall into …

On the analysis and approximation of some models of fluids over weighted spaces on convex polyhedra

E Otárola, AJ Salgado - Numerische Mathematik, 2022 - Springer
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 …

On the existence of weak solutions for the steady Baldwin-Lomax model and generalizations

LC Berselli, D Breit - Journal of Mathematical Analysis and Applications, 2021 - Elsevier
In this paper we consider the steady Baldwin-Lomax model, which is a rotational model
proposed to describe turbulent flows at statistical equilibrium. The Baldwin-Lomax model is …

A Posteriori Error Estimates for the Stationary Navier--Stokes Equations with Dirac Measures

A Allendes, E Otárola, AJ Salgado - SIAM Journal on Scientific Computing, 2020 - SIAM
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 …

Weighted estimates for generalized steady Stokes systems in nonsmooth domains

SS Byun, H So - Journal of Mathematical Physics, 2017 - pubs.aip.org
We consider a generalized steady Stokes system with discontinuous coefficients in a
nonsmooth domain when the inhomogeneous term belongs to a weighted L q space for 2< …