  Temperature stabilization of oil and gas wells is used to ensure stability
and prevent deformation of a subgrade estuary zone. In this work, we consider
the numerical simulation of thermal stabilization using vertical seasonal
freezing columns.
  A mathematical model of such problems is described by a time-dependent
temperature equation with phase transitions from water to ice. The resulting
equation is a standard nonlinear parabolic equation.
  Numerical implementation is based on the finite element method using the
package Fenics. After standard purely implicit approximation in time and simple
linearization, we obtain a system of linear algebraic equations. Because the
size of freezing columns are substantially less than the size of the modeled
area, we obtain mesh refinement near columns. Due to this, we get a large
system of equations which are solved using high performance computing systems.
