Published by De Gruyter

Volume 24 Issue 3

Issue of Journal of Numerical Mathematics

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Contents
Journal Overview

Publicly Available October 5, 2016

Frontmatter

Page range: i-iv

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Research Article

October 5, 2016

The deal.II Library, Version 8.4

Wolfgang Bangerth, Denis Davydov, Timo Heister, Luca Heltai, Guido Kanschat, Martin Kronbichler, Matthias Maier, Bruno Turcksin, David Wells

Page range: 135-141

Abstract

This paper provides an overview of the new features of the finite element library deal.II version 8.4.

Research Article

October 5, 2016

Finite element error estimates for nonlinear convective problems

Václav Kučera

Page range: 143-165

Abstract

This paper is concerned with the analysis of the finite element method applied to a nonstationary nonlinear convective problem. Using special estimates of the convective terms, we prove a priori error estimates for an explicit, semidiscrete and implicit scheme. While the explicit case is rather straightforward via mathematical induction, for the semidiscrete scheme we need to apply so-called continuous mathematical induction and a nonlinear Gronwall lemma. For the implicit scheme, we use a suitable continuation of the discrete implicit solution and again use continuous mathematical induction to prove the error estimates. Finally, we extend the presented analysis from globally Lipschitz-continuous convective nonlinearities to the locally Lipschitz-continuous case.

Research Article

October 6, 2016

Duality-based adaptivity in finite element discretization of heterogeneous multiscale problems

Matthias Maier, Rolf Rannacher

Page range: 167-187

Abstract

This paper introduces an framework for adaptivity for a class of heterogeneous multiscale finite element methods for elliptic problems, which is suitable for a posteriori error estimation with separated quantification of the model error as well as the macroscopic and microscopic discretization errors. The method is derived within a general framework for ‘goal-oriented’ adaptivity, the so-called Dual Weighted Residual (DWR) method. This allows for a systematic a posteriori balancing of multiscale modeling and discretization. The developed method is tested numerically at elliptic diffusion problems for different types of heterogeneous oscillatory coefficients.

Research Article

October 5, 2016

Sensitivity analysis of the grad-div stabilization parameter in finite element simulations of incompressible flow

Monika Neda, Faranak Pahlevani, Leo G. Rebholz, Jiajia Waters

Page range: 189-206

Abstract

We present a numerical study of the sensitivity of the grad-div stabilization parameter for mixed finite element discretizations of incompressible flow problems. For incompressible isothermal and non-isothermal Stokes equations and Navier-Stokes equations, we develop the associated sensitivity equations for changes in the grad-div parameter. Finite element schemes are devised for computing solutions to the sensitivity systems, analyzed for stability and accuracy, and finally tested on several benchmark problems. Our results reveal that solutions are most sensitive for small values of the parameter, near obstacles and corners, when the pressure is large, and when the viscosity is small.

About this journal

Objective
The Journal of Numerical Mathematics (formerly East-West Journal of Numerical Mathematics) contains high-quality papers featuring contemporary research in all areas of Numerical Mathematics. This includes the development, analysis, and implementation of new and innovative methods in Numerical Linear Algebra, Numerical Analysis, Optimal Control/Optimization, and Scientific Computing. The journal will also publish applications-oriented papers with significant mathematical content in computational fluid dynamics and other areas of computational engineering, finance, and life sciences.

Topics

Numerical Mathematics
Computational Mathematics
Applied Mathematics
Numerical Linear Algebra
Numerical Analysis
Optimal Control/Optimization
Scientific Computing
Computational Fluid Dynamics
Finance
Life Sciences

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Original research articles

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