An adaptive random feature method that repositions feature hyperplanes and collocation points according to the gradient of the current approximation resolves near-singular PDEs to high accuracy.
Thom´ ee, Galerkin Finite Element Methods for Parabolic Problems, Vol
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Adaptive feature capture method for solving partial differential equations with near singular solutions
An adaptive random feature method that repositions feature hyperplanes and collocation points according to the gradient of the current approximation resolves near-singular PDEs to high accuracy.