A note on error analysis for a nonconforming discretisation of the tri-Helmholtz equation with singular data

01/11/2021

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by   Andreas Bock, et al.

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We apply the nonconforming discretisation of Wu and Xu (2019) to the tri-Helmholtz equation on the plane where the source term is a functional evaluating the test function on a one-dimensional mesh-aligned embedded curve. We present error analysis for the convergence of the discretisation and linear convergence as a function of mesh size is recovered almost everywhere away from the embedded curve which aligns with classic regularity theory.