Abstract
We present a construction of C 1 piecewise quadratic hierarchical bases of Lagrange type on arbitrary polygonal domains Ω ⊂ R 2 . Properly normalized, these bases are Riesz bases for Sobolev spaces H s ( Ω ) , with s ∈ ( 1 , 5 2 ) . The method is applicable to arbitrary initial triangulations of polygonal domains, and does not require a checkerboard quadrangulation needed for earlier C 1 cubic hierarchical Lagrange bases. Homogeneous boundary conditions can be taken into account in a natural way, and lead to Riesz bases for Sobolev spaces H 0 s ( Ω ) , s ∈ ( 1 , 5 / 2 ) ∖ { 3 / 2 } , and H 00 3 / 2 ( Ω ) .
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