Adaptive numerical integration on spherical triangles

• Autores: Natalia Boal Sánchez , Francisco Javier Sayas González
• Localización: VIII Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques / coord. por Manuel Pedro Palacios Latasa , David Trujillo, Juan José Torrens Iñigo , Monique Madaune-Tort , María Cruz López de Silanes Busto , Gerardo Sanz Sáiz , 2003, ISBN 84-7733-720-9, págs. 61-69
• Idioma: inglés
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• Resumen

  • In this work we present an adaptive algorithm for the numerical approximation of integrals on parts of a spherical surface. The rules are constructed by dividing progressively a basic triangulation of a spherical triangle following [3] and mapping the curved triangulation to a polyhedron where integrals are approximated by simple two¿dimensional rules (see [2]).

    We show numerical evidence of the possibility of applying Richardson extrapolation to accelerate the convergence and to estimate the error. With arguments close to those used in [5] we give a formal justification of why this is possible and construct an adaptive algorithm by refining the triangulation where needed.