Implementation of hierarchical bases in FEMLAB for simplicial elements

ABSTRACT

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.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Certification and testing

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.8 Partial Differential Equations
          Subjects: Finite element methods

Keywords:
FEMLAB, condition number, finite element methods, hierarchical bases