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Multiple scales in space
• Further gains may be obtained by allowing non-conforming
meshes at the interfaces:
• Kinematic continuity has to be imposed
on the interface I . At the continuous
level in space (i.e. before discretization):
U
= U
1
I
2
I
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Multiple scales in space (2)
• We impose continuity on the discrete mesh by means of
Lagrange multipliers.
• Several alternatives are possible, depending on spatial
location (support) of multipliers.
• LBB condition must be satisfied!
– Space of multipliers should not be too rich
– Number of conditions < than total number of concerned dofs
– Too few conditions: loose coupling
– Too many conditions: singular problem or spurious “locking”
of the interface
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