An adaptive finite element discretization for Poisson's equation is proposed

What is it about?

Many engineering and physical problems modeled by partial differential equations are posed on cylindrical structures with edges. Thus the regularity of the solution and the accuracy of any numerical method of discretization are affected by the presence of the edges. In this article we • explain the use of partial Fourier analysis for simplifying the computational process, • show how the edge singularities can be computed with efficacy, • propose a new adaptation of the combined Fourier and finite element methods with optimal accuracy, • illustrate the practical implementation of the algorithm.

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Photo by Vivek Doshi on Unsplash

Photo by Vivek Doshi on Unsplash

Why is it important?

We have introduced and tested a new method for efficiently computing the flux intensity functions. We have also introduced and tested a new postprocessing strategy for the finite element method for boundary value problems in three-dimensional domains.

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