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. Author manuscript; available in PMC: 2015 Dec 1.

Published in final edited form as: J Mech Phys Solids. 2014 Dec 1;72:20–39. doi: 10.1016/j.jmps.2014.07.015

Illustration of the mechanical (left) and electrophysiological (right) Dirichlet (essential) and Neumann (natural) boundary conditions. For the mechanical problem, Dirichlet and Neumann boundary conditions are prescribed on the boundaries ∂ and ∂ , respectively. For the electrical problem, ∂ and ∂ denote the boundaries where the corresponding Dirichlet and Neumann boundary conditions are defined separately. These sub-boundaries are complementary ∂ = ∂ ∪ ∂ , ∂ = ∂ ∪ ∂ and disjoint ∂ ∩ ∂ = ∅, ∂ ∩ ∂ = ∅.

Inline graphic — Illustration of the mechanical (left) and electrophysiological (right) Dirichlet (essential) and Neumann (natural) boundary conditions. For the mechanical problem, Dirichlet and Neumann boundary conditions are prescribed on the boundaries ∂ and ∂ , respectively. For the electrical problem, ∂ and ∂ denote the boundaries where the corresponding Dirichlet and Neumann boundary conditions are defined separately. These sub-boundaries are complementary ∂ = ∂ ∪ ∂ , ∂ = ∂ ∪ ∂ and disjoint ∂ ∩ ∂ = ∅, ∂ ∩ ∂ = ∅.