20 citations · 80 across the 33 of their papers we have counts for
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A uniform additive Schwarz preconditioner for the -version of Discontinuous Galerkin approximations of elliptic problems
Paola F. Antonietti, Marco Sarti, Marco Verani +1
In this paper we design and analyze a uniform preconditioner for a class of high order Discontinuous Galerkin schemes. The preconditioner is based on a space splitting involving th…
Multigrid algorithms for -version Interior Penalty Discontinuous Galerkin methods on polygonal and polyhedral meshes
Paola F. Antonietti, Paul Houston, Xiaozhe Hu +2
In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp-version…
Contraction and optimality properties of an adaptive Legendre-Galerkin method: the multi-dimensional case
Claudio Canuto, Valeria Simoncini, Marco Verani
We analyze the theoretical properties of an adaptive Legendre-Galerkin method in the multidimensional case. After the recent investigations for Fourier-Galerkin methods in a period…
Shape optimization for Stokes flow: a reference domain approach
Ivan Fumagalli, Nicola Parolini, Marco Verani
In this paper we analyze a shape optimization problem, with Stokes equations as the state problem, defined on a domain with a part of the boundary that is described as the graph of…
High order discontinuous Galerkin methods on surfaces
Paola Antonietti, Andreas Dedner, Pravin Madhavan +3
We derive and analyze high order discontinuous Galerkin methods for second-order elliptic problems on implicitely defined surfaces in . This is done by carefully ad…