Published by De Gruyter

Volume 27 Issue 2

Issue of Journal of Numerical Mathematics

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Journal Overview

Publicly Available June 20, 2019

Frontmatter

Page range: 1-3

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March 19, 2018

On sinc quadrature approximations of fractional powers of regularly accretive operators

Andrea Bonito, Wenyu Lei, Joseph E. Pasciak

Page range: 57-68

Abstract

We consider the finite element approximation of fractional powers of regularly accretive operators via the Dunford–Taylor integral approach. We use a sinc quadrature scheme to approximate the Balakrishnan representation of the negative powers of the operator as well as its finite element approximation. We improve the exponentially convergent error estimates from [A. Bonito and J. E. Pasciak, IMA J. Numer. Anal ., 37 (2016), No. 3, 1245–1273] by reducing the regularity required on the data. Numerical experiments illustrating the new theory are provided.

January 30, 2018

Adapted explicit two-step peer methods

Dajana Conte, Raffaele D’Ambrosio, Martina Moccaldi, Beatrice Paternoster

Page range: 69-83

Abstract

In this paper, we present a general class of exponentially fitted two-step peer methods for the numerical integration of ordinary differential equations. The numerical scheme is constructed in order to exploit a-priori known information about the qualitative behaviour of the solution by adapting peer methods already known in literature. Examples of methods with 2 and 3 stages are provided. The effectiveness of this problem-oriented approach is shown through some numerical tests on well-known problems.

January 30, 2018

L²-error analysis of an isoparametric unfitted finite element method for elliptic interface problems

Christoph Lehrenfeld, Arnold Reusken

Page range: 85-99

Abstract

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method was introduced which achieves a high order approximation of the geometry for domains which are implicitly described by smooth level set functions. This method is based on a parametric mapping which transforms a piecewise planar interface (or surface) reconstruction to a high order approximation. In the paper [C. Lehrenfeld and A. Reusken, IMA J. Numer. Anal . 38 (2018), No. 3, 1351–1387] an a priori error analysis of the method applied to an interface problem is presented. The analysis reveals optimal order discretization error bounds in the H 1 -norm. In this paper we extend this analysis and derive optimal L 2 -error bounds.

Open Access January 14, 2019

Dual weighted residual error estimation for the finite cell method

Paolo Di Stolfo, Andreas Rademacher, Andreas Schröder

Page range: 101-122

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Abstract

The paper presents a goal-oriented error control based on the dual weighted residual method (DWR) for the finite cell method (FCM), which is characterized by an enclosing domain covering the domain of the problem. The error identity derived by the DWR method allows for a combined treatment of the discretization and quadrature error introduced by the FCM. We present an adaptive strategy with the aim to balance these two error contributions. Its performance is demonstrated for several two-dimensional examples.

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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Volume 27 Issue 2

Issue of Journal of Numerical Mathematics

Frontmatter

On sinc quadrature approximations of fractional powers of regularly accretive operators

Abstract

Adapted explicit two-step peer methods

Abstract

L2-error analysis of an isoparametric unfitted finite element method for elliptic interface problems

Abstract

Dual weighted residual error estimation for the finite cell method

Abstract

L²-error analysis of an isoparametric unfitted finite element method for elliptic interface problems