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We introduce a Virtual Element space <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\varPhi }_h \\subset H^2({\\varOmega })$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:mrow>\n                        <mml:msub>\n                          <mml:mi>\u03a6<\/mml:mi>\n                          <mml:mi>h<\/mml:mi>\n                        <\/mml:msub>\n                        <mml:mo>\u2282<\/mml:mo>\n                        <mml:msup>\n                          <mml:mi>H<\/mml:mi>\n                          <mml:mn>2<\/mml:mn>\n                        <\/mml:msup>\n                        <mml:mrow>\n                          <mml:mo>(<\/mml:mo>\n                          <mml:mi>\u03a9<\/mml:mi>\n                          <mml:mo>)<\/mml:mo>\n                        <\/mml:mrow>\n                      <\/mml:mrow>\n                    <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and prove that the triad <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\{{\\varPhi }_h, {\\varvec{V}}_h, Q_h\\}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:mrow>\n                        <mml:mo>{<\/mml:mo>\n                        <mml:msub>\n                          <mml:mi>\u03a6<\/mml:mi>\n                          <mml:mi>h<\/mml:mi>\n                        <\/mml:msub>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:msub>\n                          <mml:mrow>\n                            <mml:mi>V<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:mi>h<\/mml:mi>\n                        <\/mml:msub>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:msub>\n                          <mml:mi>Q<\/mml:mi>\n                          <mml:mi>h<\/mml:mi>\n                        <\/mml:msub>\n                        <mml:mo>}<\/mml:mo>\n                      <\/mml:mrow>\n                    <\/mml:math><\/jats:alternatives><\/jats:inline-formula> (with <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\varvec{V}}_h$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:msub>\n                        <mml:mrow>\n                          <mml:mi>V<\/mml:mi>\n                        <\/mml:mrow>\n                        <mml:mi>h<\/mml:mi>\n                      <\/mml:msub>\n                    <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$Q_h$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:msub>\n                        <mml:mi>Q<\/mml:mi>\n                        <mml:mi>h<\/mml:mi>\n                      <\/mml:msub>\n                    <\/mml:math><\/jats:alternatives><\/jats:inline-formula> denoting the discrete velocity and pressure spaces) is an exact Stokes complex. Furthermore, we show the computability of the associated differential operators in terms of the adopted degrees of freedom and explore also a different discretization of the convective trilinear form. The theoretical findings are supported by numerical tests.<\/jats:p>","DOI":"10.1007\/s10915-019-01049-3","type":"journal-article","created":{"date-parts":[[2019,9,13]],"date-time":"2019-09-13T20:04:46Z","timestamp":1568405086000},"page":"990-1018","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":68,"title":["The Stokes Complex for Virtual Elements with Application to Navier\u2013Stokes Flows"],"prefix":"10.1007","volume":"81","author":[{"given":"L.","family":"Beir\u00e3o da Veiga","sequence":"first","affiliation":[]},{"given":"D.","family":"Mora","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9035-5731","authenticated-orcid":false,"given":"G.","family":"Vacca","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,9,13]]},"reference":[{"key":"1049_CR1","unstructured":"Adams, R.A.: Sobolev Spaces, Volume 65 of Pure and Applied Mathematics. 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