Trefftz, collocation, and other boundary methods—a comparison
ZC Li, TT Lu, HT Huang… - Numerical Methods for …, 2007 - Wiley Online Library
In this article we survey the Trefftz method (TM), the collocation method (CM), and the
collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal …
collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal …
Singularities and treatments of elliptic boundary value problems
ZC Li, TT Lu - Mathematical and Computer Modelling, 2000 - Elsevier
This paper provides a survey for treatments for singularity problems of elliptic equations. We
take the Laplace equation on polygons as an example, and choose Motz's problem as a …
take the Laplace equation on polygons as an example, and choose Motz's problem as a …
A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain
B Fornberg, N Flyer - Proceedings of the Royal Society A …, 2011 - royalsocietypublishing.org
A recently discovered transform approach allows a large class of PDEs to be solved in terms
of boundary and/or contour integrals. We introduce here a spectrally accurate numerical …
of boundary and/or contour integrals. We introduce here a spectrally accurate numerical …
On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains
There exists a growing literature on using the Fokas method (unified transform method) to
solve Laplace and Helmholtz problems on convex polygonal domains. We show here that …
solve Laplace and Helmholtz problems on convex polygonal domains. We show here that …
[HTML][HTML] The enriched multinode Shepard collocation method for solving elliptic problems with singularities
In this paper, the multinode Shepard method is adopted for the first time to numerically solve
a differential problem with a discontinuity in the boundary. Starting from previous studies on …
a differential problem with a discontinuity in the boundary. Starting from previous studies on …
The solution of Laplacian problems over L‐shaped domains with a singular function boundary integral method
M Elliotis, G Georgiou… - … in numerical methods in …, 2002 - Wiley Online Library
The singular function boundary integral method is applied for the solution of a Laplace
equation problem over an L‐shaped domain. The solution is approximated by the leading …
equation problem over an L‐shaped domain. The solution is approximated by the leading …
Highly accurate solutions of Motz's and the cracked beam problems
For Motz's problem and the cracked beam problem, the collocation Trefftz method is used to
seek their approximate solutions u N=∑ i= 0 ND ir i+ (1/2) cos (i+ (1/2)) θ, where Di are the …
seek their approximate solutions u N=∑ i= 0 ND ir i+ (1/2) cos (i+ (1/2)) θ, where Di are the …
Solving Laplacian problems with boundary singularities: a comparison of a singular function boundary integral method with the p/hp version of the finite element …
M Elliotis, G Georgiou, C Xenophontos - Applied Mathematics and …, 2005 - Elsevier
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 …
integral method as well as the p/hp finite element method. In the former method, the solution …
Three-dimensional singular boundary elements for corner and edge singularities in potential problems
It is well known that the spatial derivative of the potential field governed by the Laplace and
Poisson equations can become infinite at corners (in two and three dimensions) and edges …
Poisson equations can become infinite at corners (in two and three dimensions) and edges …