$C^1$ error estimation on the boundary for an exterior Neumann problem in $\mathbb R^3$
In this paper we establish a \(C^1\) error estimation on the boundary for the solution of an exterior Neumann problem in \(\mathbb R^3\). To solve this problem we consider an integral representation which depends from the solution of a boundary integral equation. We use a full piecewise linear discretisation which on one hand leads to a simple numerical algorithm but on the other hand the error analysis becomes more difficult due to the singularity of the integral kernel. We construct a particular approximation for the solution of the boundary integral equation, for the solution of the Neumann problem and its gradient on the boundary and estimate their \(C^0\) error.
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