منابع مشابه
Numerical quadrature over smooth, closed surfaces.
The numerical approximation of definite integrals, or quadrature, often involves the construction of an interpolant of the integrand and its subsequent integration. In the case of one dimension it is natural to rely on polynomial interpolants. However, their extension to two or more dimensions can be costly and unstable. An efficient method for computing surface integrals on the sphere is detai...
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Performing the shape derivative (Sokolowski and Zolesio, 1992) and using the maximum principle, we show that the so-called Quadrature Surfaces free boundary problem QS ( f , k) ⎪⎪⎪⎨⎪⎪⎪⎩ −ΔuΩ = f in Ω uΩ = 0 on ∂Ω |∇uΩ| = k (constant) on ∂Ω. has a solution which contains strictly the support of f if and only if ∫
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ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 1994
ISSN: 0004-2080
DOI: 10.1007/bf02559582