INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces

The proposed method is named INTERNODES (INTERpolation for NOnconforming DEcompositionS): it can be regarded as an alternative to the mortar element method and it is simpler to implement in a numerical code. We show on two dimension al problems that by using the Lagrange interpolation we obtain at least as good convergence results as with the mortar element method with any order of polynomials. When using low order polynomials, the radial-basis interpolant leads to the same convergence properties as the Lagrange interpolant. We conclude with a comparison between INTERNODES and a standard conforming approximation in a three dimensional case.