{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:52:01Z","timestamp":1776797521580,"version":"3.51.2"},"reference-count":33,"publisher":"American Mathematical Society (AMS)","issue":"296","license":[{"start":{"date-parts":[[2016,3,30]],"date-time":"2016-03-30T00:00:00Z","timestamp":1459296000000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We construct an interpolation operator that does not increase the total variation and is defined on continuous first degree finite elements over Cartesian meshes for any dimension\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"d\">\n                        <mml:semantics>\n                          <mml:mi>d<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">d<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and right triangular meshes for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"d equals 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>d<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">d = 2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . The operator is stable and exhibits second order approximation properties in any\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                    ,\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"1 less-than-or-equal-to p less-than-or-equal-to normal infinity\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mi mathvariant=\"normal\">\n                              \u221e\n                              \n                            <\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">1\\leq p \\leq \\infty<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . With the help of it we provide improved error estimates for discrete minimizers of the total variation denoising problem and for total variation flows. We also explore computationally the limitations of the total variation diminishing property over non-Cartesian meshes.\n                  <\/p>","DOI":"10.1090\/mcom\/2942","type":"journal-article","created":{"date-parts":[[2015,3,30]],"date-time":"2015-03-30T10:50:21Z","timestamp":1427712621000},"page":"2569-2587","source":"Crossref","is-referenced-by-count":17,"title":["A total variation diminishing interpolation operator and applications"],"prefix":"10.1090","volume":"84","author":[{"given":"S\u00f6ren","family":"Bartels","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ricardo","family":"Nochetto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abner","family":"Salgado","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,3,30]]},"reference":[{"key":"1","series-title":"Oxford Mathematical Monographs","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198502456.001.0001","volume-title":"Functions of bounded variation and free discontinuity problems","author":"Ambrosio, Luigi","year":"2000","ISBN":"https:\/\/id.crossref.org\/isbn\/0198502451"},{"key":"2","series-title":"Progress in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-7928-6","volume-title":"Parabolic quasilinear equations minimizing linear growth functionals","volume":"223","author":"Andreu-Vaillo, Fuensanta","year":"2004","ISBN":"https:\/\/id.crossref.org\/isbn\/3764366192"},{"key":"3","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/BF01781073","article-title":"Pairings between measures and bounded functions and compensated compactness","volume":"135","author":"Anzellotti, Gabriele","year":"1983","journal-title":"Ann. 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