Interpolation in Finite Element Spaces

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Related lectures (31)

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Distributions & Interpolation Spaces

Explores convolution operators, interpolation spaces, and function convergence in different spaces.

Lagrange Interpolation

Introduces Lagrange interpolation for approximating data points with polynomials, discussing challenges and techniques for accurate interpolation.

Distribution to Spaces: Interpolation and Continuity

Covers weak derivatives, interpolation spaces, and continuity in function spaces.

Error Analysis and Interpolation

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Embedding in Function Spaces

Explores embedding in function spaces, including elliptic equations, Hölder inequality, Lorentz space, and Hardy-Young inequality.

Piecewise Linear Interpolation

Covers the concept of piecewise linear interpolation and the importance of dividing intervals correctly.

Distribution & Interpolation Spaces

Explores distribution and interpolation spaces, differential operators, Fourier transform, Schwartz space, fundamental solutions, Farrier transform, and uniform continuity.

Trigonometric Interpolation: Approximation of Periodic Functions and Signals

Explores trigonometric interpolation for approximating periodic functions and signals using equally spaced nodes.

Interpolation of Lagrange: Dualité and Coupling

Explores Lagrange interpolation, emphasizing uniqueness and simplicity in reconstructing functions from limited values.

Polynomial Interpolation: Optimizing Error

Covers the optimization of error in polynomial interpolation, focusing on minimizing the error by strategically placing interpolation points.