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Prediction of tissue rupture from percolation of local strain heterogeneities for diagnostics. [PDF]

open access: yesCommun Med (Lond)
Schütte F   +5 more
europepmc   +1 more source

An implementation of hp-FEM for the fractional Laplacian [PDF]

open access: yesComputers and Mathematics with Applications
We consider the discretization of the $1d$-integral Dirichlet fractional Laplacian by $hp$-finite elements. We present quadrature schemes to set up the stiffness matrix and load vector that preserve the exponential convergence of $hp$-FEM on geometric ...
Bjorn Bahr, M. Faustmann, J. M. Melenk
semanticscholar   +7 more sources
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Hierarchical proximal Galerkin: a fast hp-FEM solver for variational problems with pointwise inequality constraints

arXiv.org
We leverage the proximal Galerkin algorithm (Keith and Surowiec, Foundations of Computational Mathematics, 2024), a recently introduced mesh-independent algorithm, to obtain a high-order finite element solver for variational problems, posed on tensor ...
Ioannis P. A. Papadopoulos
semanticscholar   +1 more source

$hp$-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains

, 2020
In bounded, polygonal domains $\Omega\subset \mathbb{R}^2$ with Lipschitz boundary $\partial\Omega$ consisting of a finite number of Jordan curves admitting analytic parametrizations, we analyze $hp$-FEM discretizations of a linear, second order ...
L. Banjai, J. Melenk, C. Schwab
semanticscholar   +1 more source

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