Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity by M-decompositions

A locking-free hp DPG method for linear elasticity with symmetric stresses

We present two new methods for linear elasticity that simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p. This is achieved within the recently developed discontinuous PetrovGalerkin (DPG) framework. In this framework, both the stress and the displacement approximations are discontinuous across element interfaces. We st...

A Superconvergent HDG Method for the Maxwell Equations

We present and analyze a new hybridizable discontinuous Galerkin (HDG) method for the steady state Maxwell equations. In order to make the problem well-posed, a condition of divergence is imposed on the electric field. Then a Lagrange multiplier p is introduced, and the problem becomes the solution of a mixed curl-curl formulation of the Maxwell’s problem. We use polynomials of degree k + 1, k,...

On the modified iterative methods for $M$-matrix linear systems

This paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. Recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the Accelerated Overrelaxation (AOR) method. In this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditio...

Symmetric Chain Decompositions of Linear Lattices

ABS-Type Methods for Solving $m$ Linear Equations in $frac{m}{k}$ Steps for $k=1,2,cdots,m$

‎The ABS methods‎, ‎introduced by Abaffy‎, ‎Broyden and Spedicato‎, ‎are‎‎direct iteration methods for solving a linear system where the‎‎$i$-th iteration satisfies the first $i$ equations‎, ‎therefore a‎ ‎system of $m$ equations is solved in at most $m$ steps‎. ‎In this‎‎paper‎, ‎we introduce a class of ABS-type methods for solving a full row‎‎rank linear equations‎, ‎w...