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A-posteriori-steered $p$-robust multigrid and domain decomposition methods with optimal step-sizes for mixed finite element discretizations of elliptic problems

Autor: Miraçi, Ani, Papež, Jan, Vohralík, Martin, Yotov, Ivan

In this work, we develop algebraic solvers for linear systems arising from the discretization of second-order elliptic problems by saddle-point mixed finite element methods of arbitrary polynomial degree $p \ge 0$. We present a multigrid and a two-le

Externí odkaz: http://arxiv.org/abs/2406.09872

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A posteriori error estimates based on multilevel decompositions with large problems on the coarsest level

Autor: Vacek, Petr, Papež, Jan, Strakoš, Zdeněk

Multilevel methods represent a powerful approach in numerical solution of partial differential equations. The multilevel structure can also be used to construct estimates for total and algebraic errors of computed approximations. This paper deals wit

Externí odkaz: http://arxiv.org/abs/2405.06532

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Estimating the error in CG-like algorithms for least-squares and least-norm problems

Autor: Papež, Jan, Tichý, Petr

In [Meurant, Pape\v{z}, Tich\'y; Numerical Algorithms 88, 2021], we presented an adaptive estimate for the energy norm of the error in the conjugate gradient (CG) method. In this paper, we extend the estimate to algorithms for solving linear approxim

Externí odkaz: http://arxiv.org/abs/2305.02044

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Accurate error estimation in CG

Autor: Meurant, Gérard, Papež, Jan, Tichý, Petr

In practical computations, the (preconditioned) conjugate gradient (P)CG method is the iterative method of choice for solving systems of linear algebraic equations $Ax=b$ with a real symmetric positive definite matrix $A$. During the iterations it is

Externí odkaz: http://arxiv.org/abs/2101.03931

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