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A nonoverlapping domain decomposition method for Legendre spectral collocation problems
(2007)
We consider the Dirichlet boundary value problem for Poisson's equation in an L-shaped region or a rectangle with a cross-point. In both cases, we approximate the Dirichlet problem using Legendre spectral collocation, that ...
The method of fundamental solutions for layered elastic materials
(2001)
In this paper, we investigate the application of the method of fundamental solutions to two-dimensional elasticity problems in isotropic and anisotropic single materials and bimaterials. A domain decomposition technique ...
Matrix decomposition algorithms for modified spline collocation for Helmholtz problems
(2003)
We consider the solution of various boundary value problems for the Helmholtz equation in the unit square using a nodal cubic spline collocation method and modifications of it which produce optimal (fourth-) order ...
Analysis of the singular function boundary integral method for a biharmonic problem with one boundary singularity
(2012)
In this article, we analyze the singular function boundary integral method (SFBIM) for a two-dimensional biharmonic problem with one boundary singularity, as a model for the Newtonian stick-slip flow problem. In the SFBIM, ...
Spectral element discretization of the circular driven cavity. Part IV: The Navier-Stokes equations
(2004)
This paper deals with the spectral element discretization of the Navier-Stokes equations in a disk with discontinuous boundary data, which is known as the driven cavity problem. The numerical treatment does not involve any ...
Note on the distribution of extreme wave crests
(2005)
The sea elevation at a fixed point is modelled by means of a second order model, which is a smooth algebraic function of a vector valued Gaussian process. Asymptotic methods, presented first in [1], are used to estimate ...
Rate of convergence for vanishing viscosity approximations to hyperbolic balance laws
(2011)
The rate of convergence for vanishing viscosity approximations to hyperbolic balance laws is established. The result applies to systems that are strictly hyperbolic and genuinely nonlinear with a source term satisfying a ...
Solving Laplacian problems with boundary singularities: A comparison of a singular function boundary integral method with the p/hp version of the finite element method
(2005)
We solve a Laplacian problem over an L-shaped domain using a singular function boundary integral method as well as the p/hp finite element method. In the former method, the solution is approximated by the leading terms of ...
A singular function boundary integral method for the laplace equation
(1996)
The authors present a new singular function boundary integral method for the numerical solution of problems with singularities which is based on approximation of the solution by the leading terms of the local asymptotic ...
Solution of the planar Newtonian stick-slip problem with the singular function boundary integral method
(2005)
A singular function boundary integral method (SFBIM) is proposed for solving biharmonic problems with boundary singularities. The method is applied to the Newtonian stick-slip flow problem. The streamfunction is approximated ...