The article
"Solving the Laplace Tidal Equations using Freely Available, Easily
Extensible Finite Element Software," Granville Sewell and Vlad Manea,
Computers and Geosciences, 2021, shows how PDE2D can be used to solve the eccentricity-
or obliquity-forced Laplace tidal equations, illustrating its use on three
icy satellites of Saturn and Jupiter. Four PDE2D programs, which can be
easily modified to solve most of the problems in the article and many more,
are downloadable, and will run using the free * trial * version of PDE2D.

The four programs can be downloaded here:

- LTE_linear.f solves the Laplace tidal
equations with (linear) Rayleigh dissipation. If run without changes,
this program produces the plots seen in Figure 4 of the article, but users
can easily modify it to solve many other linear tidal dissipation problems.
The default output consists of surface plots of U,V and η at
0%,25%,50%,75%,100% of the way through the last period, and two plots
with the time-averaged geographical distribution of the tidal dissipation
rate.
- LTE_nonlinear.f solves the Laplace
tidal equations with (nonlinear) bottom drag. If run without changes,
this program produces the result seen in line 1 of Table 2 of the article
and if 'mode' is changed to 2, it produces the result of line 1 of Table 3,
but users can easily modify it to solve many other nonlinear tidal
dissipation problems. The default output consists of surface plots of
U,V and η at 0%,25%,50%,75%,100% of the way through the last period, and
two plots with the time-averaged geographical distribution of the tidal
dissipation rate.
- LTEice_linear.f solves the Laplace tidal
equations with (linear) Rayleigh dissipation, including the effects of an
ice cap. If run without changes, this program produces the plots seen in
Figure 7 of the article, but users can easily modify it to solve many
other linear tidal dissipation problems, with ice cap. The default output
consists of surface plots of U,V, η and Q at 0%,25%,50%,75%,100% of the
way through the last period, and two plots with the time-averaged geographical
distribution of the tidal dissipation rate.
- LTEice_nonlinear.f solves the Laplace tidal
equations with (nonlinear) bottom drag, including the effects of an ice cap.
If run without changes, this program produces the result for ocean depth = 100m
in Figure 8a of the article, but users can easily modify it to solve many
other nonlinear tidal dissipation problems, with ice cap. The default output
consists of surface plots of U,V, η and Q at 0%,25%,50%,75%,100% of the
way through the last period, and two plots with the time-averaged geographical
distribution of the tidal dissipation rate.