Finite-Basis Correction Velocity-Field Equations for Quarter-Domain Plane-Strain Compression Analysis Using Structured Admissible Velocity Fields

This technical supplement provides explicit Cartesian expressions for finite-basis Correction velocity fields in the Structured Admissible Velocity Field (SAVF) formulation for quarter-domain plane-strain compression. The document supplements the study presented at the JSME Yamanashi District Conference 2026 by providing detailed velocity-field equations that could not be included in the conference paper due to space limitations. Part I presents expanded expressions for 4-DOF basis sets, while Part II illustrates higher-order extensions through 8-DOF expressions, including the coupled Q9G13 construction. The Q, G, FC, LEG, BERN, CHEB, and JAC basis families are covered using SYM, ASYM, and FULL constructions.