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We provide optimal convergence error estimates, in the energy and in the weaker <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\textit{L}^\\text {2}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>L<\/mml:mi>\n                    <mml:mtext>2<\/mml:mtext>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-norm, in which the CVEM and BEM contributions to the error are separated. This allows for taking advantage of the high order flexibility of the CVEM to retrieve an accurate discrete solution by using a low order BEM. 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