I have an object with surface charge $\sigma$ for which I want to caclulate tangential electric field which would correspond to mathematical formulation:$$\vec{E}(\vec{x}) = \nabla_x \int \frac{\sigma_y}{|\vec{x} - \vec{y}|} dS_y$$where afterwards normal component $\vec{n} (\vec{E} \cdot \vec{n})$ is substracted. For now I have tried to put this surface charge on surface mesh nodes and then transforming the integral to summations (skipping singularity) assuming that integral value on triangle is average of it on nodes. In this way my calculation totally fails.As looking why it does not work I started to suspect that higly singular kernel in the integral. To overcome it I look on some different ways:Interpolating the charge density piecwise linearly and then doing the integrationPush the charges inside the suface about a size of mesh triangleWhat other options are available and which do you recommend? Also would it help if I calculate potential either of theese methods and afterwards taking derivative of it? 
Calculating tangential electric field intensity on the boundary
electromagnetism