Volume 39, Issue 2
An Arbitrary Order Reconstructed Discontinuous Approximation to Biharmonic Interface Problem

Yan Chen, Ruo Li & Qicheng Liu

Ann. Appl. Math., 39 (2023), pp. 149-180.

Published online: 2023-06

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  • Abstract

We present an arbitrary order discontinuous Galerkin finite element method for solving the biharmonic interface problem on the unfitted mesh. The approximation space is constructed by a patch reconstruction process with at most one degrees of freedom per element. The discrete problem is based on the symmetric interior penalty method and the jump conditions are weakly imposed by the Nitsche’s technique. The $C^2$-smooth interface is allowed to intersect elements in a very general fashion and the stability near the interface is naturally ensured by the patch reconstruction. We prove the optimal a priori error estimate under the energy norm and the $L^2$ norm. Numerical results are provided to verify the theoretical analysis.

  • AMS Subject Headings

65N30

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COPYRIGHT: © Global Science Press

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@Article{AAM-39-149, author = {Chen , YanLi , Ruo and Liu , Qicheng}, title = {An Arbitrary Order Reconstructed Discontinuous Approximation to Biharmonic Interface Problem}, journal = {Annals of Applied Mathematics}, year = {2023}, volume = {39}, number = {2}, pages = {149--180}, abstract = {

We present an arbitrary order discontinuous Galerkin finite element method for solving the biharmonic interface problem on the unfitted mesh. The approximation space is constructed by a patch reconstruction process with at most one degrees of freedom per element. The discrete problem is based on the symmetric interior penalty method and the jump conditions are weakly imposed by the Nitsche’s technique. The $C^2$-smooth interface is allowed to intersect elements in a very general fashion and the stability near the interface is naturally ensured by the patch reconstruction. We prove the optimal a priori error estimate under the energy norm and the $L^2$ norm. Numerical results are provided to verify the theoretical analysis.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2023-0011}, url = {http://global-sci.org/intro/article_detail/aam/21832.html} }
TY - JOUR T1 - An Arbitrary Order Reconstructed Discontinuous Approximation to Biharmonic Interface Problem AU - Chen , Yan AU - Li , Ruo AU - Liu , Qicheng JO - Annals of Applied Mathematics VL - 2 SP - 149 EP - 180 PY - 2023 DA - 2023/06 SN - 39 DO - http://doi.org/10.4208/aam.OA-2023-0011 UR - https://global-sci.org/intro/article_detail/aam/21832.html KW - Biharmonic interface problem, patch reconstruction, discontinuous Galerkin method. AB -

We present an arbitrary order discontinuous Galerkin finite element method for solving the biharmonic interface problem on the unfitted mesh. The approximation space is constructed by a patch reconstruction process with at most one degrees of freedom per element. The discrete problem is based on the symmetric interior penalty method and the jump conditions are weakly imposed by the Nitsche’s technique. The $C^2$-smooth interface is allowed to intersect elements in a very general fashion and the stability near the interface is naturally ensured by the patch reconstruction. We prove the optimal a priori error estimate under the energy norm and the $L^2$ norm. Numerical results are provided to verify the theoretical analysis.

Chen , YanLi , Ruo and Liu , Qicheng. (2023). An Arbitrary Order Reconstructed Discontinuous Approximation to Biharmonic Interface Problem. Annals of Applied Mathematics. 39 (2). 149-180. doi:10.4208/aam.OA-2023-0011
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