A bulk-surface Laplace PDE with open boundary is recast as an integro-differential equation with existence/uniqueness proven, edge singularity asymptotics derived, and a finite element method incorporating the singularity developed with rigorous error bounds confirmed numerically.
82, Springer, 2014
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Bulk-Surface Coupled PDE with an Open Boundary
A bulk-surface Laplace PDE with open boundary is recast as an integro-differential equation with existence/uniqueness proven, edge singularity asymptotics derived, and a finite element method incorporating the singularity developed with rigorous error bounds confirmed numerically.