{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T04:25:11Z","timestamp":1777091111739,"version":"3.51.4"},"reference-count":44,"publisher":"American Mathematical Society (AMS)","issue":"295","license":[{"start":{"date-parts":[[2016,2,26]],"date-time":"2016-02-26T00:00:00Z","timestamp":1456444800000},"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                    We study the approximation properties of some general finite-element spaces constructed using improved graded meshes. In our results, either the approximating function or the function to be approximated (or both) are in a weighted Sobolev space. We consider also the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L Superscript p\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mi>p<\/mml:mi>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -version of these spaces. The finite-element spaces that we define are obtained from\n                    <italic>conformally invariant<\/italic>\n                    families of finite elements (no affine invariance is used), stressing the use of elements that lead to higher regularity finite-element spaces. We prove that for a suitable grading of the meshes, one obtains the usual optimal approximation results. We provide a construction of these spaces that does not lead to long, \u201cskinny\u201d triangles. Our results are then used to obtain\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L squared\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -error estimates and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h Superscript m\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>h<\/mml:mi>\n                            <mml:mi>m<\/mml:mi>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">h^m<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -quasi-optimal rates of convergence for the FEM approximation of solutions of strongly elliptic interface\/boundary value problems.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2015-02934-2","type":"journal-article","created":{"date-parts":[[2015,2,26]],"date-time":"2015-02-26T08:11:16Z","timestamp":1424938276000},"page":"2191-2220","source":"Crossref","is-referenced-by-count":9,"title":["Graded mesh approximation in weighted Sobolev spaces and elliptic equations in 2D"],"prefix":"10.1090","volume":"84","author":[{"given":"James","family":"Adler","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Victor","family":"Nistor","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,2,26]]},"reference":[{"issue":"6","key":"1","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1002\/(SICI)1099-1476(199804)21:6<519::AID-MMA962>3.3.CO;2-I","article-title":"The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges","volume":"21","author":"Apel, Thomas","year":"1998","journal-title":"Math. 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