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A combination of a special Hermite finite element with collocation for a reaction-diffusion type equation. (English) Zbl 1422.65386

Summary: In the paper, we propose an efficient method based on the use of a bicubic Hermite finite element coupled with collocation for the reaction-diffusion equation with a variable coefficient. This enables one to reduce the dimension of the system of equations in comparison with the standard finite element scheme. Numerical experiments confirm a theoretical convergence estimate and demonstrate the advantage of the proposed method.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J15 Second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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