General error estimates are proved for a class of finite element schemes for nonstationary
thermal convection problems with temperature-dependent coefficients. These variable …

A stabilized finite element scheme for infinite Prandtl number Boussinesq equations with
temperature-dependent coefficients is analyzed. The domain is a spherical shell and the P1 …

In heat exchangers, an incompressible fluid is heated initially and cooled at the boundary.
The goal is to transfer the heat to the boundary as efficiently as possible. In this paper we …

Error estimates are introduced in a finite element approximation to thermal convection
problems with the Joule heat. From the Joule heat, a nonlinear source term arises in the …

I present in this work the GHOST (Geoscientific Hollow Sphere Tessellation) software which
allows for the fast generation of computational meshes in hollow sphere geometries …

The structure of finite element matrices in congruent subdomains is studied. When a domain
has a form of symmetries and/or periodicities, it is decomposed into a union of congruent …

In this paper, two characteristic methods are introduced to solve the thermal convection
problems with infinite Prandtl number on nonuniform staggered grids. We obtain spatial …

We investigate two models that are widely used in physics and engineering. Our main goal
is to study conjectures made by physicists with full mathematical rigor. The first model we …

The dynamics and evolution of the Earth's mantle are considered to be influenced by several
complexities of the physical processes. In order to understand the mantle convection in the …

In this chapter, we review stabilized finite element methods for the Stokes equations. The
Stokes equations describe the motion of an incompressible fluid with slow flow speed. The …