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# Recovery\-based error estimation and adaptivity using high\-order splines over hierarchical T\-meshes
Authors: Cosmin Anitescu, Md Naim Hossain, Timon Rabczuk
Source title: , 2018 () 
Academic year of acceptance: Abstract: An adaptive higher\-order method based on a generalization of
polynomial/rational splines over hierarchical T\-meshes (PHT/RHT\-splines) is
introduced. While most problems considered in isogeometric analysis can be
solved efficiently when the solution is smooth, many non\-trivial simulations
have rough solutions. This can be caused, for example, by the presence of
re\-entrant corners in the domain. For such problems, a tensor\-product basis is
less suitable for resolving the singularities that appear, as refinement
propagates throughout the computational domain. Hierarchical bases and
adaptivity allow for a more efficient way of dealing with singularities, by
adding more degrees of freedom only where they are necessary to improve the
approximation. In order to drive the adaptive refinement, an efficient
recovery\-based error estimator is proposed in this work. The estimator produces
a “recovered solution” which is a more accurate approximation than the computed
numerical solution. Several 2D and 3D numerical investigations with PHT\-splines
of higher order and greater continuity show good performance compared to uniform
refinement in terms of degrees of freedom and computational cost.
Link: <https://www.sciencedirect.com/science/article/pii/S0045782517306114>
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Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes | Khoa học - Công nghệ Nhảy đến nội dung x Đại học Tôn Đức Thắng  English Khoa học - Công nghệ Main navigation Giới thiệu Nghiên cứu Sản phẩm Nguồn lực Giảng viên/Viên chức  Sinh viên  Cựu sinh viên Search Publications Breadcrumb Trang chủ  - Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes Authors: Cosmin Anitescu, Md Naim Hossain, Timon Rabczuk Source title: ,  2018  () Academic year of acceptance: Abstract: An adaptive higher-order method based on a generalization of polynomial/rational splines over hierarchical T-meshes (PHT/RHT-splines) is introduced. While most problems considered in isogeometric analysis can be solved efficiently when the solution is smooth, many non-trivial simulations have rough solutions. This can be caused, for example, by the presence of re-entrant corners in the domain. For such problems, a tensor-product basis is less suitable for resolving the singularities that appear, as refinement propagates throughout the computational domain. Hierarchical bases and adaptivity allow for a more efficient way of dealing with singularities, by adding more degrees of freedom only where they are necessary to improve the approximation. In order to drive the adaptive refinement, an efficient recovery-based error estimator is proposed in this work. The estimator produces a “recovered solution” which is a more accurate approximation than the computed numerical solution. Several 2D and 3D numerical investigations with PHT-splines of higher order and greater continuity show good performance compared to uniform refinement in terms of degrees of freedom and computational cost. Link: https://www.sciencedirect.com/science/article/pii/S0045782517306114 Công bố mới  Bằng sáng chế  Tạp chí khoa học  Hội nghị-Hội thảo Viện nghiên cứu  Nhóm nghiên cứu  NCKH Sinh viên  NCKH Giảng viên Quỹ phát triển NCKH  Dịch vụ KHCN  Hợp tác quốc tế  Tài trợ nghiên cứu Giới thiệu  Liên hệ Đại học Tôn Đức Thắng Số 19 Nguyễn Hữu Thọ, Phường Tân Phong, Quận 7, TP. Hồ Chí Minh, Việt Nam.  Kết nối với TDTU Copyright ©  Ton Duc Thang University