Q000007: Sauter–Schwab
| Integral | \(\displaystyle \int\int f(x,y)\,\mathrm{d}x\,\mathrm{d}y\) |
| Notes | This quadrature rule is designed for functions \(f(x,y)\) that have a singularity at \(x=y\) |
| References | Sauter, Stefan A. and Schwab, Christoph. Generating the matrix coefficients, in Boundary Element Methods, 2010. [DOI: 10.1007/978-3-540-68093-2] |
Quadrilateral
Order 1
Order 2
Order 3
Order 4
(plot not shown for rule with >1000 points)
Order 5
(plot not shown for rule with >1000 points)
Edge-adjacent quadrilaterals
Order 1
Order 2
Order 3
Order 4
(plot not shown for rule with >1000 points)
Order 5
(plot not shown for rule with >1000 points)
Vertex-adjacent quadrilaterals
Order 1
Order 2
Order 3
Order 4
(plot not shown for rule with >1000 points)
Order 5
(plot not shown for rule with >1000 points)
Triangle
Order 1
Order 2
Order 3
Order 4
(plot not shown for rule with >1000 points)
Order 5
(plot not shown for rule with >1000 points)
Edge-adjacent triangle and quadrilateral
Order 1
Order 2
Order 3
Order 4
(plot not shown for rule with >1000 points)
Order 5
(plot not shown for rule with >1000 points)
Vertex-adjacent triangle and quadrilateral
Order 1
Order 2
Order 3
Order 4
Order 5
(plot not shown for rule with >1000 points)
Edge-adjacent triangles
Order 1
Order 2
Order 3
Order 4
(plot not shown for rule with >1000 points)
Order 5
(plot not shown for rule with >1000 points)
Vertex-adjacent triangles
Order 1
Order 2
Order 3
Order 4
Order 5
(plot not shown for rule with >1000 points)