<a name="Intro"></a>
<h1>Introduction</h1>
-<h2>The Boussinesq equations</h2>
+<h3>The Boussinesq equations</h3>
This program deals with an interesting physical problem: how does a
fluid (i.e. a liquid or gas) behave if it experiences differences in
-<h2>%Boundary and initial conditions</h2>
+<h3>%Boundary and initial conditions</h3>
Since the Boussinesq equations are derived under the assumption that inertia
of the fluid's motion does not play a role, the flow field is at each time
reasonable. In this program, we will use no normal flux conditions.
-<h2>Solution approach</h2>
+<h3>Solution approach</h3>
Like the equations solved in @ref step_21 "step-21", we here have a
system of differential-algebraic equations (DAE): with respect to the time
in the top-left corner of the differential operator.
-<h3>Time stepping</h3>
+<h4>Time stepping</h4>
The structure of the problem as a DAE allows us to use the same
strategy as we have already used in @ref step_21 "step-21", i.e. we
field.
-<h3>Weak form and space discretization</h3>
+<h4>Weak form and space discretization</h4>
Like solving the mixed Laplace equations, solving the Stokes equations
requires us to choose particular pairs of finite elements for
-<h3>Linear solvers</h3>
+<h4>Linear solvers</h4>
As explained above, our approach to solving the joint system for
velocities/pressure on the one hand and temperature on the other is to use an