1,721,078 research outputs found
Adaptive discretization of the stationary and incompressible Navier-Stokes equations by stabilized Finite Element Methods
Full text linkRobustness in a posteriori error estimates for the Oseen equations with general boundary conditions
No full textWe present a residual-based a posteriori error estimator for a stabilized finite element discretization of an incompressible Oseen-like model with general boundary conditions. We focus our attention on the behavior of the effectivity index and we carry out a numerical study of its sensitiveness to the problem and mesh parameters
An adaptive WEM algorithm for solving elliptic boundary value problems in fairly general domains
Full text linkIn this paper, we introduce a simple adaptive wavelet element algorithm similar to the Cohen–Dahmen–DeVore algorithm [A. Cohen, W. Dahmen, and R. DeVore, Math. Comp., 70 (2001), pp. 27–75]. The main difference is that we do not assume knowledge of the many constants appearing therein. The algorithm is easy to implement and applicable to a large class of problems in
fairly general domains. The efficiency is illustrated by several two-dimensional numerical examples and compared with an adaptive finite element method
Numerical investigation of effectivity indices of space-time error indicators for Navier-Stokes equations
No full textIn this paper we propose two error indicators aimed at estimating the space discretization error and the time discretization error for the unsteady Navier-Stokes equations. We define a space error indicator for evaluating the quality of the mesh and a time error indicator for evaluating the time discretization error. Moreover, we verify the reliability of the estimations through numerical experiments and we propose an effective space-time adaptive strategy for the unsteady Navier-Stokes equations. Such technique is based on two residual-based error indicators that suitably drive the mesh and the timestep-length modifications. Adaptive simulations show that the presented strategy allows to obtain accurate solutions in efficient wa
Two-sided a posteriori error bounds for incompressible quasi-Newtonian flows
No full textWe develop a posteriori upper and lower error bounds for mixed finite-element approximations of a general family of steady, viscous, incompressible quasi-Newtonian flows in a bounded Lipschitz domain
Ω \sub Rd ; the family includes degenerate models such as the power law model, as well as non-degenerate ones such as the Carreau model. The unified theoretical framework developed herein yields residualbased
a posteriori bounds which measure the error in the approximation of the velocity in the W1,r(Ω) norm and that of the pressure in the L^r'(Ω) norm, 1/r + 1/r' = 1, r 2 (1,∞)
Effective polygonal mesh generation and refinement for VEM
Full text linkIn the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorithm improves the numerical solution accuracy and the mesh quality through a controlled refinement strategy applied to the generic polygonal elements of the domain tessellation. The numerical results show that the outlined strategy proves to be versatile and possibly applicable to each two-dimensional problem where polygonal meshes offer advantages. In particular, we focus on the simulation of flow in fractured media, specifically using the Discrete Fracture Network (DFN) model. A residual a-posteriori error estimator tailored for the DFN case is employed. We chose this particular application to emphasize the effectiveness of the algorithm in handling complex geometries. All the numerical tests demonstrate optimal convergence rates for all the tested VEM orders
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