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We propose an HDG scheme where quasi-periodic boundary conditions are imposed on the numerical trace space. Under regularity assumptions and a proper choice of the stabilization parameter, we prove that the approximations of the electric and magnetic fields converge, in the <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\textrm{L}^2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mtext>L<\/mml:mtext>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-norm, to the exact solution with order <jats:inline-formula><jats:alternatives><jats:tex-math>$$h^{k+1}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>h<\/mml:mi>\n                    <mml:mrow>\n                      <mml:mi>k<\/mml:mi>\n                      <mml:mo>+<\/mml:mo>\n                      <mml:mn>1<\/mml:mn>\n                    <\/mml:mrow>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$h^{k+1\/2}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>h<\/mml:mi>\n                    <mml:mrow>\n                      <mml:mi>k<\/mml:mi>\n                      <mml:mo>+<\/mml:mo>\n                      <mml:mn>1<\/mml:mn>\n                      <mml:mo>\/<\/mml:mo>\n                      <mml:mn>2<\/mml:mn>\n                    <\/mml:mrow>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, resp., where <jats:italic>h<\/jats:italic> is the meshsize and <jats:italic>k<\/jats:italic> the polynomial degree of the discrete spaces. Although, numerical evidence suggests optimal order of convergence for both variables. An <jats:italic>a posteriori<\/jats:italic> error estimator for an energy norm is also proposed. We show that it is reliable and locally efficient under certain conditions. Numerical examples are provided to illustrate the performance of the quasi-periodic HDG method and the adaptive scheme based on the proposed error indicator.\n<\/jats:p>","DOI":"10.1007\/s10915-023-02367-3","type":"journal-article","created":{"date-parts":[[2023,11,22]],"date-time":"2023-11-22T06:01:35Z","timestamp":1700632895000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An Adaptive and Quasi-periodic HDG Method for Maxwell\u2019s Equations in Heterogeneous Media"],"prefix":"10.1007","volume":"98","author":[{"given":"Liliana","family":"Camargo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bibiana","family":"L\u00f3pez-Rodr\u00edguez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5359-4816","authenticated-orcid":false,"given":"Mauricio","family":"Osorio","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manuel","family":"Solano","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,11,22]]},"reference":[{"key":"2367_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cma.2012.01.005","volume":"217","author":"S Acosta","year":"2012","unstructured":"Acosta, S., Villamizar, V., Malone, B.: The DtN nonreflecting boundary condition for multiple scattering problems in the half-plane. 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