Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFortin Operator for the Taylor-Hood Element
82
0
0.0
(
0
)
Added by
Tabea Tscherpel
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We design a Fortin operator for the lowest-order Taylor-Hood element in any dimension, which was previously constructed only in 2D. In the construction we use tangential edge bubble functions for the divergence correcting operator. This naturally leads to an alternative inf-sup stable reduced finite element pair. Furthermore, we provide a counterexample to the inf-sup stability and hence to existence of a Fortin operator for the $P_2$-$P_0$ and the augmented Taylor-Hood element in 3D.
rate research
Read More
We propose a family of mixed finite element that is robust for the nearly incompressible strain gradient model, which is a fourth order singular perturbation elliptic system. The element is similar to the Taylor-Hood element in the Stokes flow. Using a uniform stable Fortin operator for the mixed finite element pairs, we are able to prove the optimal rate of convergence that is robust in the incompressible limit. Moreover, we estimate the convergence rate of the numerical solution to the unperturbed second order elliptic system. Numerical results for both smooth solutions and the solutions with sharp layers confirm the theoretical prediction.
We deal with the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) preconditioner for elliptic problems discretized by the virtual element method (VEM). We extend the result of [22] to the three dimensional case. We prove polylogarithmic condition number bounds, independent of the number of subdomains, the mesh size, and jumps in the diffusion coefficients. Numerical experiments validate the theory
In this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing the area of a surface subject to a prescribed boundary condition. We derive optimal error estimate and present several numerical tests assessing the validity of the theoretical results.
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective treatment of the different boundary conditions that arise naturally in a variational formulation. Our formulation is based on introducing the gradient of the solution as an explicit variable, constrained using a Lagrange multiplier. The essential boundary conditions are enforced weakly, using Nitsches method where required. As a result, the problem is rewritten as a saddle-point system, requiring analysis of the resulting finite-element discretization and the construction of optimal linear solvers. Here, we discuss the analysis of the well-posedness and accuracy of the finite-element formulation. Moreover, we develop monolithic multigrid solvers for the resulting linear systems. Two and three-dimensional numerical results are presented to demonstrate the accuracy of the discretization and efficiency of the multigrid solvers proposed.
Using the framework of operator or Calderon preconditioning, uniform preconditioners are constructed for elliptic operators discretized with continuous finite (or boundary) elements. The preconditioners are constructed as the composition of an opposite order operator, discretized on the same ansatz space, and two diagonal scaling operators.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
