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The double‐layer potential operator over polyhedral domains II: Spline Galerkin methods
Author(s) -
Elschner Johannes
Publication year - 1992
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670150104
Subject(s) - mathematics , piecewise , galerkin method , spline (mechanical) , mathematical analysis , operator (biology) , constant (computer programming) , polygon mesh , surface (topology) , geometry , nonlinear system , biochemistry , chemistry , structural engineering , repressor , transcription factor , engineering , gene , physics , quantum mechanics , computer science , programming language
We examine the numerical approximation of the integral equation (λ − K ) u = f , where K is the double layer (harmonic) potential operator on a closed polyhedral surface in ℝ 3 and λ, ∣λ∣≥1, is a complex constant. The solution is approximated by Galerkin's method, which is based on piecewise polynomials of arbitrary degree on graded triangulations. By utilizing spline spaces which are modified in that the trial functions vanish on some of the triangles closest to the vertices and edges, we investigate the stability of this method in L 2 . Furthermore, the use of suitably graded meshes leads to the same quasioptimal error estimates as in the case of a smooth surface.