We consider boundary element methods where the Calderón projector is used for the system matrix and boundary conditions are weakly imposed using a particular variational boundary operator designed using techniques from augmented Lagrangian methods. Regardless of the boundary conditions, both the primal trace variable and the flux are approximated. We focus on the imposition of Dirichlet, mixed Dirichlet--Neumann, and Robin conditions. A salient feature of the Robin condition is that the conditioning of the system is robust also for stiff boundary conditions. The theory is illustrated by a series of numerical examples.


  1. boundary element method
  2. weak boundary conditions
  3. mixed boundary conditions
  4. Robin conditions
  5. Calderon projection

MSC codes

  1. 65N38
  2. 65R20

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Information & Authors


Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: A1357 - A1384
ISSN (online): 1095-7197


Submitted: 25 June 2018
Accepted: 25 January 2019
Published online: 2 May 2019


  1. boundary element method
  2. weak boundary conditions
  3. mixed boundary conditions
  4. Robin conditions
  5. Calderon projection

MSC codes

  1. 65N38
  2. 65R20



Funding Information

Engineering and Physical Sciences Research Council https://doi.org/10.13039/501100000266 : EP/P01576X/1, EP/P012434/1

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