[HTML][HTML] Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection–diffusion–reaction problems
A Ern, AF Stephansen, M Vohralík - Journal of computational and applied …, 2010 - Elsevier
We propose and study a posteriori error estimates for convection–diffusion–reaction
problems with inhomogeneous and anisotropic diffusion approximated by weighted interior …
problems with inhomogeneous and anisotropic diffusion approximated by weighted interior …
A posteriori error estimates including algebraic error and stopping criteria for iterative solvers
For the finite volume discretization of a second-order elliptic model problem, we derive a
posteriori error estimates which take into account an inexact solution of the associated linear …
posteriori error estimates which take into account an inexact solution of the associated linear …
[图书][B] Finite volume methods for the incompressible Navier-stokes equations
Recently, engineers, scientists, and mathematicians have concentrated their efforts on
numerical methods for solving the Navier–Stokes equations. The reason is that these …
numerical methods for solving the Navier–Stokes equations. The reason is that these …
A posteriori error estimation based on potential and flux reconstruction for the heat equation
A Ern, M Vohralík - SIAM Journal on Numerical Analysis, 2010 - SIAM
We derive a posteriori error estimates for the discretization of the heat equation in a unified
and fully discrete setting comprising the discontinuous Galerkin, various finite volume, and …
and fully discrete setting comprising the discontinuous Galerkin, various finite volume, and …
A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra
In this paper, we develop a new mixed finite element method for elliptic problems on general
quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme …
quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme …
A review of recent advances in discretization methods, a posteriori error analysis, and adaptive algorithms for numerical modeling in geosciences
DA Di Pietro, M Vohralík - Oil & Gas Science and …, 2014 - ogst.ifpenergiesnouvelles.fr
Two research subjects in geosciences which lately underwent significant progress are
treated in this review. In the first part, we focus on one key ingredient for the numerical …
treated in this review. In the first part, we focus on one key ingredient for the numerical …
A unified framework for a posteriori error estimation for the Stokes problem
A Hannukainen, R Stenberg, M Vohralík - Numerische Mathematik, 2012 - Springer
In this paper, a unified framework for a posteriori error estimation for the Stokes problem is
developed. It is based on H^ 1_0 (Ω)^ d-conforming velocity reconstruction and H (div, Ω) …
developed. It is based on H^ 1_0 (Ω)^ d-conforming velocity reconstruction and H (div, Ω) …
A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows
M Vohralík, MF Wheeler - Computational Geosciences, 2013 - Springer
This paper develops a general abstract framework for a posteriori estimates for immiscible
incompressible two-phase flows in porous media. We measure the error by the dual norm of …
incompressible two-phase flows in porous media. We measure the error by the dual norm of …
Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods
M Vohralík - Mathematics of computation, 2010 - ams.org
We derive in this paper a unified framework for a priori and a posteriori error analysis of
mixed finite element discretizations of second-order elliptic problems. It is based on the …
mixed finite element discretizations of second-order elliptic problems. It is based on the …
A metric-based adaptive mesh refinement criterion under constrain for solving elliptic problems on quad/octree grids
In this work we propose and investigate the performance of a metric-based refinement
criteria for adaptive meshing used for improving the numerical solution of an elliptic problem …
criteria for adaptive meshing used for improving the numerical solution of an elliptic problem …