Properly constructed, Meshfree and particle methods offer exceptional flexibility in constructing discretizations and allows limitless deformations [1,2]. The Galerkin formulation of these methods has been a natural choice due to its direct correspondence with energy minimization in solid mechanics. From a mathematical standpoint, it has been successful due to the best approximation property: it also minimizes the error measured by the energy norm with respect to the generalized displacements or velocities. Nevertheless, a true minimum can be obtained by further considering the optimal selection of shape, measure, and continuity of the kernel. Therefore, a source of additional accuracy and stability in difficult simulations has remained untapped for decades. In this work, we first manually examine the effect of the support size and kernel continuity on accuracy and stability of the reproducing kernel formulation. Next, a strategy for optimizing these parameters is presented. A key issue here is the computability of the target error to be minimized: when quadrature is introduced into the Galerkin equation, the best approximation is subject to additional conditions [3]. Strategies to overcome this issue are presented, including variationally consistent integration. REFERENCES [1] P. C. Guan, S. W. Chi, J.S. Chen, T. R. Slawson and M. J. Roth, “Semi-Lagrangian reproducing kernel particle method for fragment-impact problems”, Int. J. Impact Eng., 38, 1033-1047 (2011). [2] J. Wang, M. Hillman, D. Wilmes, J. Magallanes and Y. Bazilevs, “Smoothed naturally stabilized RKPM for non-linear explicit dynamics with novel stress gradient update.” Comp. Mech., 75(1), 137-158 (2025). [3] T. Belytschko, J.S. Chen, and M. Hillman. Meshfree and particle methods: fundamentals and applications. John Wiley & Sons, 2023.