A posteriori error analysis of the boundary penalty method

The Boundary Penalty Method enforces Dirichlet boundary conditions weakly by a penalty parameter. We derive a posteriori error estimate of the L2(Ω)-norm and energy semi-norm for this method and we propose an adaptive strategy to choose the penalty parameter and the mesh parameter h by equidistributing the error between the terms in the energy semi-norm estimate. Finally, we consider three numerical examples where we successfully use the adaptive algorithm to solve the Poisson equation with both smooth and non-smooth boundary data.

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