105 citations · 358 across the 18 of their papers we have counts for
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A Simple Approach to Reliable and Robust A Posteriori Error Estimation for Singularly Perturbed Problems
Mark Ainsworth, Tomas Vejchodsky
A simple flux reconstruction for finite element solutions of reaction-diffusion problems is shown to yield fully computable upper bounds on the energy norm of error in an approxima…
Dispersive behavior of an energy-conserving discontinuous Galerkin method for the one-way wave equation
Mark Ainsworth, Guosheng Fu
The dispersive behavior of the recently proposed energy-conserving discontinuous Galerkin (DG) method by Fu and Shu [10] is analyzed and compared with the classical centered and up…
Bernstein-Bezier Bases for Tetrahedral Finite Elements
Mark Ainsworth, Guosheng Fu
We present a new set of basis functions for H(curl)-conforming, H(div)-conforming, and L2 -conforming finite elements of arbitrary order on a tetrahedron. The basis functions are e…
What Is the Fractional Laplacian?
Anna Lischke, Guofei Pang, Mamikon Gulian +8
The fractional Laplacian in R^d has multiple equivalent characterizations. Moreover, in bounded domains, boundary conditions must be incorporated in these characterizations in math…