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A central goal of our approach is to ensure that these properties are preserved at the discrete level while avoiding the challenges typically encountered when constructing finite element subspaces of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$H^2(\\Omega )$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\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>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    as would be required in a standard continuous Galerkin framework. At the continuous level, we establish well-posedness and characterize the solution through energy laws and mass conservation. For the semi-discrete formulation, we derive error estimates in various B\u00f4chner spaces. Furthermore, we establish that the implicit fully discrete scheme is well-posed, converges with optimal order and consistent with both mass conservation and an entropy dissipation law. Finally, we confirm the theoretical findings and conservation properties on a set of benchmark problems.\n                  <\/jats:p>","DOI":"10.1007\/s10915-026-03242-7","type":"journal-article","created":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T11:11:25Z","timestamp":1773832285000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A conservative Mixed Finite Element Method for a Regularised Nonlinear Long-Wave Model"],"prefix":"10.1007","volume":"107","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9924-3445","authenticated-orcid":false,"given":"Ankur","family":"Ankur","sequence":"first","affiliation":[]},{"given":"Andrea","family":"Cangiani","sequence":"additional","affiliation":[]},{"given":"Ram","family":"Jiwari","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,3,18]]},"reference":[{"key":"3242_CR1","doi-asserted-by":"publisher","first-page":"1345","DOI":"10.1007\/s11071-019-04858-1","volume":"96","author":"M Abbaszadeh","year":"2019","unstructured":"Abbaszadeh, M., Dehghan, M.: The interpolating element-free Galerkin method for solving Korteweg-de Vries-Rosenau-regularized long-wave equation with error analysis. 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