On Simplified Hybrid Methods for Coupling of Finite Elements and Boundary Elements

  • J. J. Grannell
Part of the Boundary Elements IX book series (BOUNDARY, volume 9/1)


Hybrid finite element methods are characterized by the use of elements which are non-conforming and for which interelement continuity conditions are enforced a-posteriori through independent fields (Lagrange multipliers) defined on interelement boundaries. Simplified hybrid methods are derived from hybrid methods by replacing the multipliers by expressions involving the element interior fields alone (through the Euler equations for the multipliers). In particular, simplified hybrid methods have been proposed to couple indirect boundary integral equation methods and also edge function methods to finite element methods. Both the edge function and indirect boundary integral methods essentially involve the representation of the approximate solution in the special boundary element by a series expansion of analytical solutions of the field equations which are tailored to deal with numerical problems which pose difficulties for conventional finite elements. Typical examples of the latter include singularities, high field gradients and infinite regions. These problems could, of course, be handled using hybrid methods. The appeal of the simplified hybrid methods lies in the avoidance of rank conditions (cf. Brezzi11, Babuska et a1.3,4, Oden33, Oden and Reddy34) and also in the resulting economy.


Boundary Element Hybrid Method Boundary Element Method Conventional Finite Element Indirect Boundary 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • J. J. Grannell
    • 1
  1. 1.Department of Mathematical PhysicsUniversity College CorkCorkIreland

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