105 citations · 293 across the 6 of their papers we have counts for
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math.NA2017★ 41 cited
Hybrid Finite Element - Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver
Mark Ainsworth, Christian Glusa
A numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed ove…
math.NA2017★ 105 cited
Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver
Mark Ainsworth, Christian Glusa
We develop all of the components needed to construct an adaptive finite element code that can be used to approximate fractional partial differential equations, on non-trivial domai…
math.NA2017★ 66 cited
Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains
Mark Ainsworth, Christian Glusa
We explore the connection between fractional order partial differential equations in two or more spatial dimensions with boundary integral operators to develop techniques that enab…