Optimal Approximation in Sobolev Spaces: A New Approach of Spline Functions
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Key Points
This article aims to explore the optimal approximation properties of spline functions within Sobolev spaces, particularly for solving partial differential equations.
Examined spline functions in relation to Sobolev spaces and embedding theorems.
Conducted numerical experiments on sample PDE problems.
Analyzed the compatibility of piecewise polynomials with boundary conditions.
Spline functions achieved comparable or better accuracy than classical methods with fewer degrees of freedom.
Showed improvements in numerical stability and solution accuracy.
Combined with isogeometric analysis, reduced computational costs while maintaining high accuracy.
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Implication
Article examines spline functions' optimal approximation in Sobolev spaces, suggesting improvements for PDE solutions.