Implementation of hierarchical bases in FEMLAB for simplicial elements

We present the implementation of well-conditioned hierarchical bases for one-dimensional, triangular and tetrahedral elements in finite element FEMLAB software. Using the domain mesh information provided by FEMLAB, we found an easy way to maintain the continuity of solution across the interelement boundaries. The conditionings of the global stiffness matrices of several standard problems are compared with the Lagrange bases and are smaller for all cases. Categories and Subject Descriptors: G.4 [Mathematical Software]--Certification and testing; G.1.8 [Numerical Analysis]: Partial Differential Equation--Finite element methods General Terms: Algorithms, Performance Additional Key Words and Phrases: FEMLAB, hierarchical bases, condition number, finite element methods