We present a mesoscopic approach to crystal plasticity based on a Landau-type theory that inherently respects the global invariance of the energy in the space of strain tensors while accommodating an infinite number of equivalent energy wells [1,2]. This framework eliminates arbitrariness in handling topological transitions for dislocation interaction, offering a robust foundation for modeling plastic deformation. However, the large deformations associated with plastic jumps introduce significant numerical challenges due to excessive mesh distortion. In this work, we propose a novel numerical solution technique designed to address these issues, ensuring stable and accurate simulations of crystal plasticity at the mesoscopic scale. [1] Landau-type theory of planar crystal plasticity, R. Baggio, O.U. Salman, Physical Review Letters 123 (20), 205501 [2] Inelastic rotations and pseudoturbulent plastic avalanches in crystals R. Baggio, O.U. Salman, L Truskinovsky Physical Review E 107 (2), 025004