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New shape functions for triangular \(p\)-FEM using integrated Jacobi polynomials. (English) Zbl 1095.65101

The authors report a remarkable result concerning the computational cost in evaluating the element stiffness matrix and element mass matrix in the \(p\)-version of finite element method (FEM) applied to a linear second-order elliptic boundary value problem. In case of piecewise constant coefficient equations they construct a two dimensional basis functions such that the matrix vector multiplication and the generation of stiffness and mass matrices can be done in a number of arithmetic operations which equals the order of the number of elements in the finite element space.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N15 Error bounds for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65Y20 Complexity and performance of numerical algorithms

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