Extension operators for trimmed spline spaces
Erik Burman, Peter Hansbo, Mats G. Larson, Karl Larsson
Abstract
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.
Topics & Concepts
MathematicsSpline (mechanical)Extension (predicate logic)PiecewisePolynomialOperator (biology)Projection (relational algebra)Algebra over a fieldApplied mathematicsMathematical analysisPure mathematicsAlgorithmComputer scienceGeneStructural engineeringRepressorTranscription factorEngineeringChemistryBiochemistryProgramming languageAdvanced Numerical Analysis TechniquesNumerical methods in engineeringAdvanced Numerical Methods in Computational Mathematics