Related papers: Fuzzy and interval finite element method for heat …
A finite element method for solving nonlinear differential equations on a grid, with potential applicability to computational fluid dynamics (CFD), is developed and tested. The current method facilitates the computation of solutions of a…
The aim of this article is to discuss the estimation of the diffusivity coefficient of a homogeneous metal rod from temperature values at a fixed point in the bar for different time instants. The time-dependent problem of heat conduction is…
As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we…
The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…
We develop a finite element method for a large deformation membrane elasticity problem on meshed surfaces using a tangential differential calculus approach that avoids the use of classical differential geometric methods. The method is also…
An important requirement in the standard finite element method (FEM) is that all elements in the underlying mesh must be tangle-free i.e., the Jacobian must be positive throughout each element. To relax this requirement, an isoparametric…
We prove strong convergence for a large class of finite element methods for the time-dependent Joule heating problem in three spatial dimensions with mixed boundary conditions on Lipschitz domains. We consider conforming subspaces for the…
Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…
This paper discusses a class of uncertain optimization problems, in which unknown parameters are modeled by fuzzy intervals. The membership functions of the fuzzy intervals are interpreted as possibility distributions for the values of the…
Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at…
In this thesis we develop a stabilised finite element method for solving the equations of poroelasticity to enable solving complex models of biological tissues such as the human lungs. For the proposed numerical scheme, we use the lowest…
The Poisson--Boltzmann equation is widely used to model electrostatics in molecular systems. Available software packages solve it using finite difference, finite element, and boundary element methods, where the latter is attractive due to…
We study a nonlocal diffusion equation of porous medium type featuring a generalised fractional pressure with spatial anisotropy. We construct a finite element method for the numerical solution of the equation on a bounded open Lipschitz…
Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation…
The solution of a momentum conservation equation for the gas and liquid stream in the flowing element is obtained on the basis of the modern approach to a problem on contact interaction of bodies and mediums. A flowing element, system are:…
This paper presents the Finite Element Method for Cosserat plates. The mathematical model for Cosserat elastic plates is based on the calculation of the optimal value of the splitting parameter. We discuss the existence and uniqueness of…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
Adaptive methods for derivation of analytical and numerical solutions of heat diffusion in one dimensional thin rod have investigated. Comperhensive comparsion analysis based on the homotopy perturbation method (HPM) and finite difference…
This study aims to present the error and numerical blow up analyses of a finite element method for computing the radially symmetric solutions of semilinear heat equations. In particular, this study establishes optimal order error estimates…