Extension operators for trimmed spline spaces

• We develop a discrete extension operator for trimmed spline spaces consisting of piecewise polynomial functions of degree p with k continuous derivatives. The construction is based on polynomial extension from neighboring elements together with projection back into the spline space. We prove stability and approximation results for the extension operator. Finally, we illustrate how we can use the extension operator to construct a stable cut isogeometric method for an elliptic model problem.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Nyckelord

Splines

A-stable

Approximation results

Cut isogeometric method

Discrete extension operator

Extension operators

Piecewise polynomial functions

Spline space

Stability results

Trimmed spline space

Unfitted finite element method

Finite element method

Cut isogeometric methods

Discrete extension operators

Trimmed spline spaces

Unfitted finite element methods

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