Journal•ISSN: 0036-1429
SIAM Journal on Numerical Analysis
Society for Industrial and Applied Mathematics
About: SIAM Journal on Numerical Analysis is an academic journal published by Society for Industrial and Applied Mathematics. The journal publishes majorly in the area(s): Finite element method & Numerical analysis. It has an ISSN identifier of 0036-1429. Over the lifetime, 5749 publications have been published receiving 354966 citations. The journal is also known as: Society for Industrial and Applied Mathematics journal on numerical analysis.
Topics: Finite element method, Numerical analysis, Discretization, Partial differential equation, Boundary value problem
Papers published on a yearly basis
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3,383 citations
TL;DR: In this paper, a framework for the analysis of a large class of discontinuous Galerkin methods for second-order elliptic problems is provided, which allows for the understanding and comparison of most of the discontinuous methods that have been proposed over the past three decades.
Abstract: We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment of elliptic problems.
3,293 citations
TL;DR: In this article, a new version of the Perona and Malik theory for edge detection and image restoration is proposed, which keeps all the improvements of the original model and avoids its drawbacks.
Abstract: A new version of the Perona and Malik theory for edge detection and image restoration is proposed. This new version keeps all the improvements of the original model and avoids its drawbacks: it is proved to be stable in presence of noise, with existence and uniqueness results. Numerical experiments on natural images are presented.
2,565 citations
TL;DR: The technique of obtaining high resolution, second order, oscillation free (TVD), explicit scalar difference schemes, by the addition of a limited antidiffusive flux to a first order scheme is described in this article.
Abstract: The technique of obtaining high resolution, second order, oscillation free (TVD), explicit scalar difference schemes, by the addition of a limited antidiffusive flux to a first order scheme is expl...
2,490 citations
TL;DR: It is proven that for scalar equations, the LDG methods are L2-stable in the nonlinear case and in the linear case, it is shown that if polynomials of degree k are used, the methods are kth order accurate for general triangulations.
Abstract: In this paper, we study the local discontinuous Galerkin (LDG) methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge--Kutta discontinuous Galerkin (RKDG) methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, high-order formal accuracy, and easy handling of complicated geometries for convection-dominated problems. It is proven that for scalar equations, the LDG methods are L2-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are kth order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.
2,265 citations