منابع مشابه
Contouring Curved Quadratic Elements
We show how to extract a contour line (or isosurface) from quadratic elements—specifically from quadratic triangles and tetrahedra. We also devise how to transform the resulting contour line (or surface) into a quartic curve (or surface) based on a curved-triangle (curved-tetrahedron) mapping. A contour in a bivariate quadratic function defined over a triangle in parameter space is a conic sect...
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Quadratic and higher order finite elements are interesting candidates for the numerical solution of (elliptic) partial differential equations (PDEs) due to their improved approximation properties in comparison to linear approaches. While the systems of equations that arise from the discretisation of the underlying PDEs are often solved by iterative schemes like preconditioned Krylow-space metho...
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Interpolation techniques are used to estimate function values and their derivatives at those points for which a numerical solution of any equation is not explicitly evaluated. In particular, the shape functions are used to interpolate a solution (within an element) of a partial differential equation obtained by the finite element method. Mesh generation and quality improvement are often driven ...
متن کاملInteractive Soft Object Simulation with Quadratic Finite Elements
We present a new method to simulate deformable volumetric objects interactively using finite elements. With quadratic basis functions and a non-linear strain tensor, we are able to model realistic local compression as well as large global deformation. The construction of the differential equations is described in detail including the Jacobian matrix required to solve the non-linear system. The ...
متن کاملBivariate C1 Quadratic Finite Elements and Vertex Splines
Following work of Heindl and of Powell and Sabin, each triangle of an arbitrary (regular) triangulation A of a polygonal region ii in R is subdivided into twelve triangles, using the three medians, yielding the refinement A of A , so that C quadratic finite elements can be constructed. In this paper, we derive the Bézier nets of these elements in terms of the parameters that describe function a...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1995
ISSN: 0377-0427
DOI: 10.1016/0377-0427(95)00061-5