The Laplace equation with discontinuous boundary data: Convergence of the spectral element discretization
SourceComptes Rendus de l'Academie des Sciences - Series I: Mathematics
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We prove an existence result for the Laplace equation in a disk with discontinuous Dirichlet boundary conditions: 0 on part of the boundary and 1 on its complement. The problem is discretized by the mortar spectral element method and a convergence estimate is derived which is confirmed numerically.