Print element quality metrics for improved debugging

Problem

Element quality metrics are not provided by the solver, so it is difficult to understand the relation between convergence and mesh properties.

Solution

Please add a parameter to the solver xml to perform a mesh quality check. This could include quality metrics applicable to multiple element types including min/max Jacobian, aspect ratio, dihedral angle, etc. In addition, metrics related to the flow, (e.g., Peclet number) or the structure (max/min stiffness matrix diagonals) would facilitate debugging. The distributions of such quantities in a mesh should be printed, for example dividing the range of Jacobian/aspect ratio etc. in (say) 10 intervals, and computing the percentage of elements belonging to each interval. An option to specify a user-defined range should be added to avoid problems with outliers or boundary layer elements.

Additional context

No response

Code of Conduct

• I agree to follow this project's Code of Conduct and Contributing Guidelines

No file, test, or entry point is named. First map how solver XML parameters are handled and where mesh and element data are available; define the supported metrics, ranges, and distribution output before implementation. Done means an XML-controlled check reports documented metric distributions for relevant element types without disrupting solver runs.