This paper deals with the numerical analysis of an upscaled model describing the reactive flow in a porous medium. The solutes are transported by advection and diffusion and undergo precipitation and dissolution. The reaction term and, in particular, the dissolution term have a particular, multivalued character, which leads to stiff dissolution fronts. We consider the Euler implicit method for ...

This paper deals with the stability of nite di erence approximations of initial value problems for the wave equation with absorbing boundary conditions. The stability of a family of high order variational numerical schemes is studied by energy techniques. Dirichlet, sponge and rst order paraxial absorbing boundary conditions are treated. The variational form of the schemes as well as the use of...

* Correspondence: zulianglux@126. com College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, PR China Full list of author information is available at the end of the article Abstract In this article, we investigate a priori error estimates for the optimal control problems governed by elliptic equations using higher order variational discretization and mixed finite elem...

The goal of this short course is to review the analysis and the systematic discretization of saddlepoint systems that arise in the weak formulation of certain fluid flow problems by Galekrin methods. To demonstrate the applicability of the main arguments in various situations, we consider the slow flow of water through a channel surrounded by a porous aquiver. While the free flow of the fluid m...

In this paper, we consider the discretization of the Stokes problem on domain partitions with non-matching meshes. We propose a hybrid mortar method, which is motivated by a variational characterization of solutions of the corresponding interface problem. For the discretization of the subdomain problems, we utilize standard inf-sup stable finite element pairs. The introduction of additional unk...

A new error control finite element formulation is developed and implemented based on the variational multiscale method, the inclusion theory in homogenization, and the Zienkiewicz–Zhu error estimator. By synthesizing variational multiscale method in computational mechanics, the equivalent eigenstrain principle in micromechanics, and the Zienkiewicz–Zhu error estimator in the finite element meth...

In this paper we investigate a variational discretization for the class of mechanical systems in presence of symmetries described by the action of a Lie group which reduces the phase space to a (non-trivial) principal bundle. By introducing a discrete connection we are able to obtain the discrete constrained higher-order Lagrange-Poincar\'e equations. These equations describe the dynamics of a ...

Polarizable continuum models (PCMs) are a widely used family of implicit solvent models based on reaction-field theory and boundary-element discretization of the solute/continuum interface. An often overlooked aspect of these theories is that discretization of the interface typically does not afford a continuous potential energy surface for the solute. In addition, we show that discretization c...