{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T11:01:21Z","timestamp":1776769281950,"version":"3.51.2"},"reference-count":26,"publisher":"American Mathematical Society (AMS)","issue":"230","license":[{"start":{"date-parts":[[2000,2,26]],"date-time":"2000-02-26T00:00:00Z","timestamp":951523200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    The mortar finite element is an example of a non-conforming method which can be used to decompose and re-compose a domain into subdomains without requiring compatibility between the meshes on the separate components. We obtain stability and convergence results for this method that are\n                    <italic>uniform<\/italic>\n                    in terms of\n                    <italic>both<\/italic>\n                    the degree\n                    <italic>and<\/italic>\n                    the mesh used, without assuming quasiuniformity for the meshes. Our results establish that the method is\n                    <italic>optimal<\/italic>\n                    when non-quasiuniform\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h\">\n                        <mml:semantics>\n                          <mml:mi>h<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">h<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    or\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h p\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>h<\/mml:mi>\n                            <mml:mi>p<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">hp<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    methods are used. Such methods are essential in practice for good rates of convergence when the interface passes through a corner of the domain. We also give an error estimate for when the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p\">\n                        <mml:semantics>\n                          <mml:mi>p<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    version is used. Numerical results for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h comma p\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>h<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>p<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">h,p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h p\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>h<\/mml:mi>\n                            <mml:mi>p<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">hp<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    mortar FEMs show that these methods behave as well as conforming FEMs. An\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h p\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>h<\/mml:mi>\n                            <mml:mi>p<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">hp<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    extension theorem is also proved.\n                  <\/p>","DOI":"10.1090\/s0025-5718-99-01083-2","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:17:31Z","timestamp":1027707451000},"page":"521-546","source":"Crossref","is-referenced-by-count":38,"title":["Uniform \u210e\ud835\udc5d convergence results for the mortar finite element method"],"prefix":"10.1090","volume":"69","author":[{"given":"Padmanabhan","family":"Seshaiyer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manil","family":"Suri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[1999,2,26]]},"reference":[{"key":"1","unstructured":"M. A. Aminpour, S. L. McClearly, J. B. Ransom. A global\/local analysis method for treating details in structural design. Proceedings of the Third NASA Advanced Composites Technology Conference, NASA CP-3178, Vol 1, Part 2, 967-986, 1992."},{"issue":"3","key":"2","doi-asserted-by":"publisher","first-page":"624","DOI":"10.1137\/0728034","article-title":"Efficient preconditioning for the \ud835\udc5d-version finite element method in two dimensions","volume":"28","author":"Babu\u0161ka, I.","year":"1991","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"4","key":"3","doi-asserted-by":"publisher","first-page":"750","DOI":"10.1137\/0724049","article-title":"The optimal convergence rate of the \ud835\udc5d-version of the finite element method","volume":"24","author":"Babu\u0161ka, I.","year":"1987","journal-title":"SIAM J. Numer. 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