On a conservation upwind finite element scheme for convective diffusion equations
On the blow-up set for non-Newtonian equation with a nonlinear boundary condition.
On the Charney Conjecture of Data Assimilation Employing Temperature Measurements Alone: The Paradigm of 3D Planetary Geostrophic Model
Analyzing the validity and success of a data assimilation algorithmwhen some state variable observations are not available is an important problem in meteorology and engineering. We present an improved data assimilation algorithm for recovering the exact full reference solution (i.e. the velocity and temperature) of the 3D Planetary Geostrophic model, at an exponential rate in time, by employing coarse spatial mesh observations of the temperature alone. This provides, in the case of this paradigm,...
On the convergence of multigrid methods for flow problems.
On the existence of weak solutions of boundary value problems in a diffusion model for an inhomogeneous liquid in regions with moving boundaries
On the Numerical Approximation of Finite Speed Diffusion Problems.
On the solution of a differential equation occurring in the problem of heat convection in laminar flow through a tube with slip-flow.
On the Transport-Diffusion Algorithm and Its Applications to the NavierStokes Equations.
Optimal control and numerical adaptivity for advection–diffusion equations
We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from splitting...
Optimal control and numerical adaptivity for advection–diffusion equations
We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the Lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from...
Optimal Convective Heat-Transport
The one-dimensional steady-state convection-diffusion problem for the unknown temperature of a medium entering the interval with the temperature and flowing with a positive velocity is studied. The medium is being heated with an intensity corresponding to for a constant . We are looking for a velocity with a given average such that the outflow temperature is maximal and discuss the influence of the boundary condition at the point on the “maximizing” function .