A Development of an Explicit Finite Element Method with Hermite Elements for 3-D Advection Equations

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  • 3次元移流方程式に対するHermite要素を用いた陽的有限要素法の開発

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This paper presents a new characteristic finite element formulation, named SLG (semi-Lagrange Galerkin) method, on unstructured triangle / tetrahedral meshes to solve two- or three-dimensional advection equations / hyperbolic flow problems. In the present method, the calculation procedure is divided into two phases which are advection and non-advection phases. The advection phase is computed by the semi-Lagrange procedure using a 10 or 20 degrees of freedom triangular / tetrahedral element which consists of complete cubic polynomials given by function values and first order derivatives on each vertex and a function value on barycenter of triangle surface. The non-advection phase is calculated by the Galerkin finite element procedure using the 3 DOF triangular or 4 DOF tetrahedral linear elements.

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