Particle tracking velocimetry produces scattered velocity samples that must be reconstructed into continuous fields before quantities such as vorticity and pressure can be evaluated. Standard post-processing methods do not enforce mass conservation, and the resulting non-physical divergence contaminates derived quantities such as pressure.

This thesis develops a constrained least-squares reconstruction method based on mimetic spectral elements. The velocity is represented in H(div), the discrete divergence-free constraint is imposed exactly as a hard algebraic constraint in a saddle-point system, and the vorticity, streamfunction, and pressure are recovered through weak formulations using the same set of discrete differential operators.

The method is verified using a manufactured solution. The measured convergence rates under both p- and h-refinement match the theoretical predictions for all five reconstructed quantities. The method is then applied to three regions of separated flow over a surface-mounted cube using experimental particle tracking data. The reconstructed velocity is divergence-free to machine precision in all cases, while the streamfunction, vorticity, and pressure fields capture the boundary-layer separation, recirculation, and shear-layer features observed in the reference data.