An adaptive octree finite element method for PDEs posed on surfaces

摘要: Abstract The paper develops a finite element method for partial differential equations posed on hypersurfaces in R N , = 2 3 . uses traces of bulk functions surface embedded volumetric domain. space is defined an octree grid which locally refined or coarsened depending error indicators and estimated values the curvatures. cartesian structure mesh leads to easy efficient adaptation process, while trace makes fitting unnecessary. number degrees freedom involved computations consistent with two-dimension nature PDEs. No parametrization required; it can be given implicitly by level set function. In practice, variant marching cubes used recover second order accuracy. We prove optimal accuracy H 1 L norms problem smooth solution quasi-uniform refinement. Experiments less regular problems demonstrate convergence respect freedom, if based appropriate indicator. shows results numerical experiments variety geometries problems, including advection–diffusion surfaces. Analysis suggest that combination adaptive meshes unfitted (trace) elements provide simple, efficient, reliable tool treatment PDEs