Hadamard product nonlinear formulation of Galerkin and finite element methods

1999/04/28 by W. Chen, Chen, W.
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Computational Engineering #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Computer and information sciences #FOS: Mathematics #Finance #G.1.2 #G.1.3 #G.1.5 #G.1.8 #Numerical Analysis (math.NA) #and Science (cs.CE)

paper · pdf · doi:10.48550/arxiv.cs/9904021

openalex publication_date 1999/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A novel nonlinear formulation of the finite element and Galerkin methods is presented here, which leads to the Hadamard product expression of the resultant nonlinear algebraic analogue. The presented formulation attains the advantages of weak formulation in the standard finite element and Galerkin schemes and avoids the costly repeated numerical integration of the Jacobian matrix via the recently developed SJT product approach. This also provides possibility of the nonlinear decoupling computations.

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