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.
Elliott and Thomas Ranner,Finite element analysis for a coupled bulk-surface partial differential equation, IMA Journal of Numerical Analysis33(2013), no
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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.