Each secondary node follows the main surface under it as the weighted average
u_A = sum_J (M_AJ / sum_K M_AK) u_J with M_AJ = int psi_A N_J over the reference overlaps and
psi the secondary faces' dual shape functions (Wohlmuth 2000), so the secondary mortar
matrix is diagonal; the rows join the couplings' constraint elimination in every implicit
analysis. Uncovered secondary nodes stay free with a warning; heat transfer and explicit
dynamics refuse ties by name. Tested by the tie patch test on non-matching hex8/tet4 meshes.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo