TY - JOUR
T1 - A priori and a posteriori error analysis of an unfitted HDG method for semi-linear elliptic problems
AU - Sánchez, Nestor
AU - Sánchez-Vizuet, Tonatiuh
AU - Solano, Manuel E.
N1 - Funding Information:
Nestor Sánchez is supported by the Scholarship Program of CONICYT-Chile. Tonatiuh Sánchez-Vizuet was partially funded by the US Department of Energy. Grant No. DE-FG02-86ER53233. Manuel E. Solano was partially funded by CONICYT–Chile through FONDECYT project No. 1200569 and by Project AFB170001 of the PIA Program: Concurso Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/8
Y1 - 2021/8
N2 - We present a priori and a posteriori error analysis of a high order hybridizable discontinuous Galerkin (HDG) method applied to a semi-linear elliptic problem posed on a piecewise curved, non polygonal domain. We approximate Ω by a polygonal subdomain Ω h and propose an HDG discretization, which is shown to be optimal under mild assumptions related to the non-linear source term and the distance between the boundaries of the polygonal subdomain Ω h and the true domain Ω. Moreover, a local non-linear post-processing of the scalar unknown is proposed and shown to provide an additional order of convergence. A reliable and locally efficient a posteriori error estimator that takes into account the error in the approximation of the boundary data of Ω h is also provided.
AB - We present a priori and a posteriori error analysis of a high order hybridizable discontinuous Galerkin (HDG) method applied to a semi-linear elliptic problem posed on a piecewise curved, non polygonal domain. We approximate Ω by a polygonal subdomain Ω h and propose an HDG discretization, which is shown to be optimal under mild assumptions related to the non-linear source term and the distance between the boundaries of the polygonal subdomain Ω h and the true domain Ω. Moreover, a local non-linear post-processing of the scalar unknown is proposed and shown to provide an additional order of convergence. A reliable and locally efficient a posteriori error estimator that takes into account the error in the approximation of the boundary data of Ω h is also provided.
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U2 - 10.1007/s00211-021-01221-8
DO - 10.1007/s00211-021-01221-8
M3 - Article
AN - SCOPUS:85112027679
SN - 0029-599X
VL - 148
SP - 919
EP - 958
JO - Numerische Mathematik
JF - Numerische Mathematik
IS - 4
ER -