A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem

By Frédéric Gibou, Ronald Fedkiw. 2005

287 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/26ffec19ba95b2db3ad321ad598b6b60e561de08

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In Computational Mechanics

In Electrical and Electronic Engineering

In Numerical Analysis

Citations in the corpus

Spatially adaptive techniques for level set methods and incompressible flow (2006, methodology): “Using the GFM, these level set algorithms have been extended to detonations and deflagrations [34], mixed compressible and incompressible flow [11], twophase incompressible flow [50, 54], low speed flames [65], Stefan problems for crystal growth [39, 38, 37], free surface flows [30], etc.”
High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources (2006, background): “Recently, some high order immersed boundary schemes have been proposed in the literature [ 15 ,33].”
A cartesian grid embedded boundary method for the heat equation and poisson's equation in three dimensions (2004, methodology): “This differs from the approach used in [5] in that we do not extrapolate in the direction of the normal.”
A level set based sharp interface method for the multiphase incompressible Navier-Stokes equations with phase change (2007, methodology): “Numerical schemes using higher order extrapolations have also been presented in Gibou and Fedkiw [ 11 ].”
A review of level-set methods and some recent applications (2018, methodology): “The GFM idea has also been applied to the case where one wants to treat Dirichlet boundary conditions [107, 108] with application to the Stefan problem [109] and has been refined in order to treat jump boundary conditions with higher accuracy [76].”
Linear Algebra and its Applications (2010, unknown): “However, for Maxwell problems for which (2.7) holds stability can be concluded from the 2 × 2-model (2.11).”