The Bogner-Fox-Schmit rectangular element is one of the simplest elements that provide continuous differentiability of an approximate solution in the framework of the finite element method. However, it can be applied ...The Bogner-Fox-Schmit rectangular element is one of the simplest elements that provide continuous differentiability of an approximate solution in the framework of the finite element method. However, it can be applied only on a simple domain composed of rectangles or parallelograms whose sides are parallel to two different straight lines. We propose a new triangular Hermite element with 13 degrees of freedom. It is used in combination with the Bogner-Fox-Schmit element near the boundary of an arbitrary polygonal domain and provides continuous differentiability of an approximate solution in the whole domain up to the boundary.展开更多
We study the extensions of the Bogner-Fox-Schmit element to the whole family of Q_(k) continuously differentiable finite elements on rectangular grids,for all k≥3,in 2D and 3D.We show that the newly defined C_(1) spa...We study the extensions of the Bogner-Fox-Schmit element to the whole family of Q_(k) continuously differentiable finite elements on rectangular grids,for all k≥3,in 2D and 3D.We show that the newly defined C_(1) spaces are maximal in the sense that they contain all C_(1)-Q_(k) functions of piecewise polynomials.We give examples of other extensions of C_(1)-Q_(k) elements.The result is consistent with the Strang’s conjecture(restricted to the quadrilateral grids in 2D and 3D).Some numerical results are provided on the family of C_(1) elements solving the biharmonic equation.展开更多
文摘The Bogner-Fox-Schmit rectangular element is one of the simplest elements that provide continuous differentiability of an approximate solution in the framework of the finite element method. However, it can be applied only on a simple domain composed of rectangles or parallelograms whose sides are parallel to two different straight lines. We propose a new triangular Hermite element with 13 degrees of freedom. It is used in combination with the Bogner-Fox-Schmit element near the boundary of an arbitrary polygonal domain and provides continuous differentiability of an approximate solution in the whole domain up to the boundary.
文摘We study the extensions of the Bogner-Fox-Schmit element to the whole family of Q_(k) continuously differentiable finite elements on rectangular grids,for all k≥3,in 2D and 3D.We show that the newly defined C_(1) spaces are maximal in the sense that they contain all C_(1)-Q_(k) functions of piecewise polynomials.We give examples of other extensions of C_(1)-Q_(k) elements.The result is consistent with the Strang’s conjecture(restricted to the quadrilateral grids in 2D and 3D).Some numerical results are provided on the family of C_(1) elements solving the biharmonic equation.
