• quadrature;
  • numerical integration;
  • level set method;
  • discontinuous Galerkin;
  • implicit surface;
  • discontinuous enrichment


We present a simple, tree-based approach for the numerical integration over volumes and surfaces defined by the zero iso-contour of a level set function. The work is motivated by a variant of the discontinuous Galerkin method that is characterized by discontinuous enrichments of the polynomial basis. Although numerical results suggest that the presently achieved accuracy is comparable with methods based on discretized delta functions and on the geometric reconstruction of the interface, the presented approach is conceptually simpler and applicable to almost arbitrary grid types, which we demonstrate by means of numerical experiments on triangular, quadrilateral, tetrahedral and hexahedral meshes. Copyright © 2012 John Wiley & Sons, Ltd.