Results 1  10
of
357
Preconditioning in H(div) and Applications
 Math. Comp
, 1998
"... . We consider the solution of the system of linear algebraic equations which arises from the finite element discretization of boundary value problems associated to the differential operator I \Gamma grad div. The natural setting for such problems is in the Hilbert space H(div) and the variational fo ..."
Abstract

Cited by 46 (5 self)
 Add to MetaCart
to precondition iterative methods so that any given error reduction may be achieved in a finite number of iterations, with the number independent of the mesh discretization. We describe applications of these results to the efficient solution of mixed and least squares finite element approximations of elliptic
1 Preconditioning in H(div) and Applications
"... Abstract. Summarizing the work of [AFW97], we show how to construct preconditioners using domain decomposition and multigrid techniques for the system of linear algebraic equations which arises from the finite element discretization of boundary value problems associated to the differential operator ..."
Abstract
 Add to MetaCart
I − grad div. These preconditioners are shown to be spectrally equivalent to the inverse of the operator and thus may be used to precondition iterative methods so that any given error reduction may be achieved in a finite number of iterations independent of the mesh discretization. We describe
Multigrid in H(div) and H(curl)
 NUMER. MATH.
, 2000
"... We consider the solution of systems of linear algebraic equations which arise from the finite element discretization of variational problems posed in the Hilbert spaces H(div) and H(curl) in three dimensions. We show that if appropriate finite element spaces and appropriate additive or multiplicati ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We consider the solution of systems of linear algebraic equations which arise from the finite element discretization of variational problems posed in the Hilbert spaces H(div) and H(curl) in three dimensions. We show that if appropriate finite element spaces and appropriate additive
DESIGN AND CONVERGENCE OF AFEM IN H(DIV)
, 2007
"... We design an adaptive finite element method (AFEM) for mixed boundary value problems associated with the differential operator A −∇div in H(div, Ω). For A being a variable coefficient matrix with possible jump discontinuities, we provide a complete a posteriori error analysis which applies to both R ..."
Abstract
 Add to MetaCart
We design an adaptive finite element method (AFEM) for mixed boundary value problems associated with the differential operator A −∇div in H(div, Ω). For A being a variable coefficient matrix with possible jump discontinuities, we provide a complete a posteriori error analysis which applies to both
COMPATIBLE GAUGE APPROACHES FOR H(div) EQUATIONS
"... Abstract. We are concerned with the compatible gauge reformulation for H(div) equations and the design of fast solvers of the resulting linear algebraic systems as in [5]. We propose an algebraic reformulation of the discrete H(div) equations along with an algebraic multigrid (AMG) technique for the ..."
Abstract
 Add to MetaCart
Abstract. We are concerned with the compatible gauge reformulation for H(div) equations and the design of fast solvers of the resulting linear algebraic systems as in [5]. We propose an algebraic reformulation of the discrete H(div) equations along with an algebraic multigrid (AMG) technique
Optimal multilevel methods for H(grad), H(curl), and H(div) systems on graded and unstructured grids
 In Multiscale, Nonlinear and Adaptive Approximation
, 2009
"... Abstract We give an overview of multilevel methods, such as Vcycle multigrid and BPX preconditioner, for solving various partial differential equations (including H(grad), H(curl) and H(div) systems) on quasiuniform meshes and extend them to graded meshes and completely unstructured grids. We firs ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
Abstract We give an overview of multilevel methods, such as Vcycle multigrid and BPX preconditioner, for solving various partial differential equations (including H(grad), H(curl) and H(div) systems) on quasiuniform meshes and extend them to graded meshes and completely unstructured grids. We
Article electronically published on May 19, 2000 WAVELET BASES IN H(div) AND H(curl)
"... Abstract. Some years ago, compactly supported divergencefree wavelets were constructed which also gave rise to a stable (biorthogonal) wavelet splitting of H(div; Ω). These bases have successfully been used both in the analysis and numerical treatment of the Stokes and Navier–Stokes equations. In t ..."
Abstract
 Add to MetaCart
Abstract. Some years ago, compactly supported divergencefree wavelets were constructed which also gave rise to a stable (biorthogonal) wavelet splitting of H(div; Ω). These bases have successfully been used both in the analysis and numerical treatment of the Stokes and Navier–Stokes equations
Preconditioning for Heterogeneous Problems
"... Summary. The main focus of this paper is to suggest a domain decomposition method for mixed finite element approximations of elliptic problems with anisotropic coefficients in domains. The theorems on traces of functions from Sobolev spaces play an important role in studying boundary value problems ..."
Abstract
 Add to MetaCart
Summary. The main focus of this paper is to suggest a domain decomposition method for mixed finite element approximations of elliptic problems with anisotropic coefficients in domains. The theorems on traces of functions from Sobolev spaces play an important role in studying boundary value problems of partial differential equations. These theorems are commonly used for a priori estimates of the stability with respect to boundary conditions, and also play very important role in constructing and studying effective domain decomposition methods. The trace theorem for anisotropic rectangles with anisotropic grids is the main tool in this paper to construct domain decomposition preconditioners. 1
BlackBox Preconditioning For Mixed Formulation . . .
, 2002
"... Mixed finite element approximation of selfadjoint elliptic PDEs leads to symmetric indefinite linear systems of equations. Preconditioning strategies commonly focus on reduced symmetric positive definite systems and require nested iteration. This deficiency is avoided if preconditioned minres is ap ..."
Abstract
 Add to MetaCart
Mixed finite element approximation of selfadjoint elliptic PDEs leads to symmetric indefinite linear systems of equations. Preconditioning strategies commonly focus on reduced symmetric positive definite systems and require nested iteration. This deficiency is avoided if preconditioned minres
Results 1  10
of
357