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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 ...
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 ...
Comparison of two methods for the computation of singular solutions in elliptic problems
(1997)
We compare two numerical methods for the solution of elliptic problems with boundary singularities. The first is the integrated singular basis function method (ISBFM), a finite-element method in which the solution is ...
A note on the convergence rate of the finite element method for singularly perturbed problems using the Shishkin mesh
(2003)
We consider the numerical approximation of singularly perturbed problems by the h version of the finite element method on a piecewise uniform, Shishkin mesh. It is well known that this method yields uniform approximations, ...
A note on p/hp finite element methods for reaction-diffusion problems in polygonal domains
(2000)
We present guidelines on how to choose the mesh and polynomial degree distribution for the approximation of reaction-diffusion problems in polygonal domains, in the context of the hp finite element method. These guidelines ...
A singular function boundary integral method for laplacian problems with boundary singularities
(2006)
A singular function boundary integral method for Laplacian problems with boundary singularities is analyzed. In this method, the solution is approximated by the truncated asymptotic expansion for the solution near the ...