Fix application related issues

[jijn]

• Please check if the PR fulfills these requirements

• The PR follows our guidelines (formatting & style)
• Tests for the changes have been added (for bug fixes / features)
• Docs have been added / updated (for bug fixes / features)

• What kind of change does this PR introduce? (Bug fix, feature, docs update, ...)
  Bug fix and docs update.

• What is the current behavior? (You can also link to an open issue here)
  See Issues related to the applications code #771

• What is the new behavior (if this is a feature change)?
  See Issues related to the applications code #771

• Does this PR introduce a breaking change? (What changes might users need to make in their application due to this PR?)
  No

• Other information:
  NA

[jijn]

Fix #771 issue 1
Files under tests/ were not modified to ensure consistency with existing output.txt

[jijn]

The notation $\nabla^2$ is used for the Laplacian to distinguish it from the increment operator $\Delta$.

[jijn]

I am done with this PR. Let me know if you have any questions.

[landinjm]

This looks good. I'll fix the precommit and merge in a few hours