{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:35:37Z","timestamp":1787337337590,"version":"build-2736575974"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01 LM011300-01"],"award-info":[{"award-number":["R01 LM011300-01"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1117695"],"award-info":[{"award-number":["CCF-1117695"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>Convolving the output of discontinuous Galerkin (DG) computations using spline filters can improve both smoothness and accuracy of the output. At domain boundaries, these filters have to be one-sided for nonperiodic boundary conditions. Recently, position-dependent smoothness-increasing accuracy-conserving (PSIAC) filters were shown to be a superset of the well-known one-sided RLKV and SRV filters. Since PSIAC filters can be formulated symbolically, PSIAC filtering amounts to forming linear products with local DG output and so offers a more stable and efficient implementation. The paper introduces a new class of PSIAC filters, NP$_0$, that have small support and are piecewise constant. Extensive numerical experiments for the canonical hyperbolic test equation show NP$_0$ filters outperform the more complex known boundary filters. NP$_0$ filters typically reduce the $L^\\infty$ error in the boundary region below that of the interior where optimally superconvergent symmetric filters of the same support are applied. NP$_0$ filtering can be implemented as forming linear combinations of the data with short rational weights. The rational filter matrices are explicitly listed for DG degree 1, 2, and 3. Exact derivatives of the convolved output are easy to compute.<\/jats:p>","DOI":"10.1137\/17m1114016","type":"journal-article","created":{"date-parts":[[2017,8,30]],"date-time":"2017-08-30T18:59:56Z","timestamp":1504119596000},"page":"A1741-A1765","source":"Crossref","is-referenced-by-count":0,"title":["Explicit Least-Degree Boundary Filters for Discontinuous Galerkin"],"prefix":"10.1137","volume":"39","author":[{"given":"Dang-Manh","family":"Nguyen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00f6rg","family":"Peters","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,8,30]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1977-0431744-9"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-02-01464-3"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/B978-044451104-1\/50007-1"},{"key":"atypb4","first-page":"46","volume":"1","author":"de Boor C.W.","year":"2005","journal-title":"Surv. 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