[Bug]: heat_nonlinear demo: the L2 error against the exact solution grows to 4.7 at t = 0.2 #610

What happened?

finite-volume-heat-nonlinear (demos/FiniteVolume/heat_nonlinear.cpp) prints the L2 error against its exact solution at each iteration. With the default options (implicit scheme, --dt 0.0001, --Tf 1), the error starts at 8.23e-05, reaches 1.02 at t = 0.1 and 4.71 at t = 0.2, then decreases to 0.28 at t = 1. The same growth happens on a uniform mesh: with --min-level 6 --max-level 6, the error is 1.02 at t = 0.1 and 4.76 at t = 0.2. An error of order one means the computed solution and the exact solution of the demo do not agree: either the scheme or the exact solution coded in the demo is wrong.

Input code

./finite-volume-heat-nonlinear
./finite-volume-heat-nonlinear --min-level 6 --max-level 6 --Tf 0.2

What expected?

An L2 error that stays at the level of the discretization error (around 1e-4 to 1e-3 here) for the whole run.

Relevant log output

iteration 0: t = 0.00, dt = 0.0001, L2-error: 8.23e-05
iteration 1000: t = 0.10, dt = 0.0001, L2-error: 1.02e+00
iteration 2000: t = 0.20, dt = 0.0001, L2-error: 4.71e+00
iteration 3000: t = 0.30, dt = 0.0001, L2-error: 9.32e-02
iteration 5000: t = 0.50, dt = 0.0001, L2-error: 2.21e-01
iteration 10000: t = 1.00, dt = 9.37138414829411e-14, L2-error: 2.80e-01

What is your operating system?

Linux

How did you install our software?

from source

Software version

main at a1bdf4e8

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