ﻻ يوجد ملخص باللغة العربية
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 mean that the heat source is allowed to belong to $H^{-1}(varpi,Omega)$, where $varpi$ is a weight in the Muckenhoupt class $A_2$ that is regular near the boundary. We propose a finite element scheme and, under the assumption that the domain is convex and $varpi^{-1} in A_1$, show its convergence. In the case that the thermal diffusion and viscosity are constants, we propose an a posteriori error estimator and show its reliability and local efficiency.
In two dimensions, we show existence of solutions to the stationary Navier Stokes equations on weighted spaces $mathbf{H}^1_0(omega,Omega) times L^2(omega,Omega)$, where the weight belongs to the Muckenhoupt class $A_2$. We show how this theory can b
We consider the periodic initial-value problem for the Serre equations of water-wave theory and its semidiscrete approximation in the space of smooth periodic polynomial splines. We prove that the semidiscrete problem is well posed, locally in time,
A direct reconstruction algorithm based on Calderons linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic inverse condu
A Morley-Wang-Xu (MWX) element method with a simply modified right hand side is proposed for a fourth order elliptic singular perturbation problem, in which the discrete bilinear form is standard as usual nonconforming finite element methods. The sha
In this paper we consider the numerical solution of Boussinesq-Peregrine type systems by the application of the Galerkin finite element method. The structure of the Boussinesq systems is explained and certain alternative nonlinear and dispersive term