Complementary polynomial families are introduced to construct C^m finite element bases of order p >= 2m+2, with explicit formulas on canonical intervals, an extended interpolation error formula, and a superconvergence result for linear problems in H^{m+1}.
Voit,Some lower bounds for distances of roots of classical orthogonal polynomials, preprint, 2022, arXiv:2109.14999
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Complementary families of approximating polynomials with applications to finite element methods applied to differential equations of arbitrary even spatial order
Complementary polynomial families are introduced to construct C^m finite element bases of order p >= 2m+2, with explicit formulas on canonical intervals, an extended interpolation error formula, and a superconvergence result for linear problems in H^{m+1}.