Tóm tắt:

In this paper, we present p-adaptive meshing algorithms (p-refinement and unrefinement) for triangular finite element meshes. The algorithms are designed to keep the computation cost low, and the neighboring elements are not too different in degree. In addition, we can prove that if we start with an admissible mesh, then each element can be refined at most once using the proposed algorithms. This is important because after a p-refinement there is no way to estimate its error without resolving the whole problem.