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Full-Text Articles in Applied Mathematics
Boundary Quadrature Formulas And Their Applications, Tian-Xiao He
Boundary Quadrature Formulas And Their Applications, Tian-Xiao He
Tian-Xiao He
This chapter surveys the analytical approach for constructing multivariate numerical integration formulas that use only boundary points as evaluation points. The applications of boundary quadrature formulas to boundary value problems of partial differential equations are also discussed.
C1 Quadratic Macroelements And C1 Orthogonal Multiresolution Analyses In 2d, Tian-Xiao He
C1 Quadratic Macroelements And C1 Orthogonal Multiresolution Analyses In 2d, Tian-Xiao He
Tian-Xiao He
Each triangle of an arbitrary regular triangulation Δ of a polygonal region in R2 is subdivided into twelve subtriangles by using three connecting lines joining three arbitrarily chosen points on its edges, three connecting lines from an arbitrarily chosen interior point in the triangle to its three vertices, and three connecting lines joining the points on the edges and the interior point. In this refinement, C1 quadratic finite elements can be constructed. In this paper, we will give explicit Bezier coefficients of elements in terms of the parameters that describe function and first partial derivative values at vertices …