An efficient finite element method for treating singularities in Laplace's equation
TL;DR: In this article, a new finite element method for solving partial differential equations with singularities caused by abrupt changes in boundary conditions or sudden change in boundary shape is presented, which eliminates the need for high-order integration, improves the overall accuracy, and yields very accurate estimates for the singular coefftcients.
read more
About: This article is published in Journal of Computational Physics. The article was published on 01 Oct 1991. and is currently open access. The article focuses on the topics: Boundary knot method & Singular boundary method.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
Marta D'Elia,Max D. Gunzburger +1 more
TL;DR: In this article, a nonlocal vector calculus is exploited to define a weak formulation of the nonlocal diffusion operator, and it is shown that, when sufficient conditions on certain kernel functions hold, the solution of such a non-local equation converges to a solution of the fractional Laplacian equation on bounded domains.
227
A coupled meshless finite point/Peridynamic method for 2D dynamic fracture analysis
TL;DR: In this article, a coupled meshless method for 2D transient elastodynamic problems involving dynamic crack propagation is developed based on an efficient coupling between the finite point method (FPM) and a discretized form of Peridynamics.
139
A coupling approach of state-based peridynamics with node-based smoothed finite element method
Y.H. Bie,Xiangyang Cui,Z.C. Li +2 more
TL;DR: In this paper, a novel approach to couple ordinary state-based peridynamics (OSPD) with node-based smoothed finite element method (NS-FEM) is proposed, where the physical information is transmitted mutually from local to non-local regions, which is governed by the unified coupling equations of motion.
108
Methods of fundamental solutions for harmonic and biharmonic boundary value problems
TL;DR: In this paper, the use of the Method of Fundamental Solutions (MFS) for solving elliptic partial differential equations is investigated, and the performance of various least squares routines used for the solution of the resulting minimization problem is studied.
Singularities and treatments of elliptic boundary value problems
TL;DR: In this article, a survey of treatments for singularity problems of elliptic equations of polygons is provided, where the authors take the Laplace equation on polygons as an example, and choose Motz's problem as a benchmark of singularity problem.
84
References
•Book
Finite element procedures in engineering analysis
Klaus-Jürgen Bathe,H. Saunders +1 more
- 01 Jan 1982
TL;DR: Elements finis Reference Record created on 2004-09-07, modified on 2016-08-08.
5.6K
The finite element method with Lagrangian multipliers
TL;DR: In this article, the Dirichlet problem for second order differential equations is chosen as a model problem to show how the finite element method may be implemented to avoid difficulty in fulfilling essential (stable) boundary conditions.
1.7K
•Book
Finite elements in fluids
Richard H. Gallagher,T. J. Chung +1 more
- 01 Jan 1975
TL;DR: In this paper, the Navier-Stokes Equations were used to model the flow of two Incompressible Non-miscible Viscous Fluids, and the Finite Element method was used to compute the flow.