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arXiv · 2506.14800

A micromorphic-based artificial diffusion method for stabilized finite element approximation of convection-diffusion problems

Soheil Firooz·B. Daya Reddy·Paul Steinmann
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Abstract

We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary variable, which is related to the gradient of the field of interest, and which leads to a coupled problem. Conditions for well-posedness of the resulting formulation are established. We carry out a comprehensive numerical study to compare the proposed methodology against some well-established approaches in one- and two-dimensional settings. The proposed method outperforms established approaches in general in approximating accurately the solutions to pertinent and challenging problems.

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Soheil Firooz, B. Daya Reddy, Paul Steinmann. 2025-06-02. A micromorphic-based artificial diffusion method for stabilized finite element approximation of convection-diffusion problems. https://arxiv.org/abs/2506.14800

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