Applications of a finite element discretisation of thin plate splines

Abstract

The thin plate spline method is a widely used data fitting technique which has the ability to smooth noisy data. We present some example applications of a new mixed finite element discretisation of the thin plate spline method. The new approach works with a pair of bases for the gradient and the Lagrange multiplier forming a biorthogonal system, thus ensuring that the scheme is numerically efficient and the formulation is stable. We overview of the theoretical foundations of the new approach and give numerical examples in both two and three dimensions. References

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