LAUSR

Meshfree methods for solid mechanics have been in development since the early 1990’s. Initial motivations included alleviation of the burden of mesh creation and the desire to overcome the limitations of traditional mesh-based discretizations for extreme deformation applications. Here, the accuracy and robustness of both meshfree and mesh-based Lagrangian discretizations are compared using manufactured extreme deformation fields. For the meshfree discretizations, both moving least squares and maximum entropy are considered. Quantitative error and convergence results are presented for the best approximation in the $$H^1$$ H 1 norm.