Higher order triangular basis functions and solution performance of the CG method

New sets of hierarchical higher order basis functions in FEM for triangle elements are constructed using a systematic orthogonalization approach that yield better conditioning and investigated with different preconditioners: Jacobi, ICC, ILU, and SAINV. Presented theoretical and numerical results indicate that certain preconditioners are insensitive to the condition number of the basis functions. Advantageous properties of basis functions in relation to preconditioners are viewed from the perspective of similarity and congruence transforms of the basis functions. This provides an alternative view for a systematic construction of the basis functions that couples with a specific preconditioner to optimize the solution performance.