A Clough-Tocher Type Element Useful for Fourth Order Problems
نویسندگان
چکیده
A new macro-element useful for finite element approximations to fourth order elliptic problems with curved boundaries is presented. An error analysis is given 2 which shows that these elements achieve 0(h ) accuracy in energy.
منابع مشابه
Interpolation Error Estimates for the Reduced Hsieh - Clough - Tocher Triangle
We study the unisolvence and interpolation properties of the reduced Hsieh-Clough-Tocher triangle. This finite element of class C , which has only nine degrees of freedom, can be used in the numerical approximation of plate problems. Introduction; Main Notation. The space R" is equipped with the Euclidean norm | • | and inner-product <•,•>. If B is a subset of R", we let hB = diameter of B, pB ...
متن کاملSimplex–Splines on the Clough–Tocher Element
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau...
متن کاملA C1 Multivariate Clough–Tocher Interpolant
We show that in dimensions four and higher, to insure a smooth interpolant, additional geometric constraints must be imposed on the generalized Clough–Tocher split introduced in Worsey and Farin (Constr. Approx. 3:99–110, 1987).
متن کاملWatertight conversion of trimmed CAD surfaces to Clough-Tocher splines
The boundary representations (B-reps) that are used to represent shape in Computer-Aided Design systems create unavoidable gaps at the face boundaries of a model. Although these inconsistencies can be kept below the scale that is important for visualisation and manufacture, they cause problems for many downstream tasks, making it difficult to use CAD models directly for simulation or advanced g...
متن کاملMacro-elements and stable local bases for splines on Clough-Tocher triangulations
Macro-elements of arbitrary smoothness are constructed on Clough-Tocher triangle splits. These elements can be used for solving boundary-value problems or for interpolation of Hermite data, and are shown to be optimal with respect to spline degree. We believe they are also optimal with respect to the number of degrees of freedom. The construction provides local bases for certain superspline spa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010