105 citations · 358 across the 18 of their papers we have counts for
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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…
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…
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…
Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations
Mark Ainsworth, Guosheng Fu
We derive a posteriori error estimates for the hybridizable discontinuous Galerkin (HDG) methods, including both the primal and mixed formulations, for the approximation of a linea…
A lowest-order composite finite element exact sequence on pyramids
Mark Ainsworth, Guosheng Fu
Composite basis functions for pyramidal elements on the spaces , , and are presented. In particular, we construct the lowes…