ABSTRACT
In this chapter we deal with the integration over regular surfaces Σ, i.e., boundary surfaces Σ = ∂ G https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315195674/823ed023-dd6c-41bb-a456-22174b64a780/content/imath16_1.tif"/> of regular regions G ⊂ ℝ 3 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315195674/823ed023-dd6c-41bb-a456-22174b64a780/content/imath16_2.tif"/> . Integration over regular surfaces (manifolds) has seen a renewed interest during the last years (see, e.g., I. Pesenson [2015] and the references therein). Different to integration over spheres is the problem that the system of eigenfunctions of the Beltrami operator on a general surface Σ is not explicitly known, which seriously limits the applicability in numerical practice. In addition, the determination of the null space of the Beltrami operator causes difficulties.
