Publication

hp-Optimal discontinuous Galerkin methods for linear elliptic problems

2007
Reports

Abstract

The aim of this paper is to overcome the well-known lack of p-optimality in hp-version discontinuous Galerkin (DG) discretizations for the numerical approximation of linear elliptic problems. For this purpose, we shall present and analyze a class of hp-DG methods that is closely related to other DG schemes, however, combines both p-optimal jump penalty as well as lifting stabilization. We will prove that the resulting error estimates are optimal with respect to both the local element sizes and polynomial degrees.

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2007
Reports

Abstract

Official source

Related concepts (32)

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Numerical integration

In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.

Numerical stability

In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.

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hp-Optimal discontinuous Galerkin methods for linear elliptic problems

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