Related papers: Error estimate for a homogenization problem involv…
In this work is considered a spectral problem, involving a second order term on the domain boundary: the Laplace-Beltrami operator. A variational formulation is presented, leading to a finite element discretization. For the Laplace-Beltrami…
Homogenization method is used to analyse the equivalent behavior of transient flow of a passive solute through highly heterogeneous porous media. The flow is governed by a coupled system which includes an elliptic equation and a linear…
We consider a stochastic process of heat conduction where energy is redistributed along a chain between nearest neighbor sites via an improper beta distribution. Similar to the well-known Kipnis-Marchioro-Presutti (KMP) model, the finite…
In this contribution we present the first formulation of a heterogeneous multiscale method for an incompressible immiscible two-phase flow system with degenerate permeabilities. The method is in a general formulation which includes…
We approximate the solution of the equation $$ -\Delta_S u+u = f $$ on a two-dimensional, embedded, orientable, closed surface $S$ where $-\Delta_S$ denotes the Laplace Beltrami operator on $S$ by using continuous, piecewise linear finite…
We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…
The design of heat exchanger fields is a key phase to ensure the long-term sustainability of such renewable energy systems. This task has to be accomplished by modelling the relevant processes in the complex system made up of different…
We study temperature distribution in a heat conducting problem, for a system of p-Laplace equation, giving rise to a free boundary.
The conformation and the phase diagram of a membrane protein are investigated via grand canonical ensemble approach using a homopolymer model. We discuss the nature and pathway of $\alpha$-helix integration into the membrane that results…
This paper considers the problem of heat transfer in a composite ceramic material where the structural elements are bonded to the matrix via a thin heat resistant adhesive layer. The layer has the form of a circular ring or close to it.…
The paper describes combinatorial synthesis approach with interval multset estimates of system elements for modeling, analysis, design, and improvement of a modular telemetry system. Morphological (modular) system design and improvement are…
Accurately simulating coupled physical processes under uncertainty is essential for reliable modeling and design in performance-critical applications such as combustion systems. Ablative heat shield design, as a specific example of this…
The present paper deals with the homogenization of the heat conduction which takes place in a binary three-dimensional medium consisting of an ambiental phase having conductivity of unity order and a rectangular honeycomb structure formed…
The divergence of the heat conductivity in the thermodynamic limit is investigated in 2d-lattice models of anharmonic solids with nearest-neighbour interaction from single-well potentials. Two different numerical approaches based on…
This paper presents a homogenization framework for elastomeric metamaterials exhibiting long-range correlated fluctuation fields. Based on full-scale numerical simulations on a class of such materials, an ansatz is proposed that allows to…
A new homogenization approach for the simulation of multi-phase flows in heterogeneous porous media is presented. It is based on the lattice Boltzmann method and combines the grayscale with the multi-component Shan-Chen method. Thus, it…
We consider the monodomain model, a system of a parabolic semilinear reaction-diffusion equation coupled with a nonlinear ordinary differential equation, arising from the (simplified) mathematical description of the electrical activity of…
We show that a certain error estimate for a fully discrete finite element approximation of the solution of the heat equation which is defined in a two-dimensional Euclidean domain carries over to the case of a general linear parabolic…
This article provides a brief introduction to the a posteriori error analysis of parabolic partial differential equations, with an emphasis on challenges distinct from those of steady-state problems. Using the heat equation as a model…
We develop error estimates for the finite element approximation of elliptic partial differential equations on perturbed domains, i.e. when the computational domain does not match the real geometry. The result shows that the error related to…