Substructuring Preconditioning for Finite Element Approximations of Second Order Elliptic Problems. Ii. Mixed Method for an Elliptic Operator with Scalar Tensor

Substructuring Preconditioning for Finite Element Approximations of Second Order Elliptic Problems I Nonconforming Linear Elements for the Poisson Equation in a Parallelepiped

Mixed Finite Elements for Elliptic Problems with Tensor Coeecients as Cell-centered Finite Diierences Mixed Finite Elements for Elliptic Problems with Tensor Coefficients as Cell-centered Finite Differences

We present an expanded mixed nite element approximation of second order elliptic problems containing a tensor coeecient. The mixed method is expanded in the sense that three variables are explicitly approximated, namely, the scalar unknown, the negative of its gradient, and its ux (the tensor coeecient times the negative gradient). The resulting linear system is a saddle point problem. In the c...

Expanded mixed finite element methods for linear second-order elliptic problems, I

We develop a new mixed formulation for the numencal solution of second-order elliptic problems This new formulation expands the standard mixed formulation in the sense that three variables are exphcitly treated the scalar unknown, its gradient, and its flux (the coefficient times the gradient) Based on this formulation, mixed finite element approximations of the second-order elliptic problems a...

Expanded mixed finite element methods for quasilinear second order elliptic problems, II

A new mixed formulation recently proposed for linear problems is extended to quasilinear second order elliptic problems This new formulation expands the standard mixed formulation in the sense that three variables are explicitly treated i e the scalar unknown its gradient and its ux the coe cients times the gradient Based on this formulation mixed nite element approximations of the quasilinear ...

Substructuring Preconditioner for Nonconforming Finite Element Approximations of Second Order Elliptic Problems with Anisotropy

Abstract In this paper an algebraic substructuring preconditioner is considered for nonconforming nite element approximations of second order elliptic problems in D domains with diagonal anisotropic di usion tensor Using a block Gauss elimination and a substructuring idea part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent matrix Whe...