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arXiv · 2411.12687

Quantum-assisted h{\lambda}-adaptive finite element method

R. H. Drebotiy·H. A. Shynkarenko
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Abstract

We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error control and corresponding approximation refinement. Appropriate finite element a posteriori error estimates are proved. Described approach demonstrates the possibility to overcome singular perturbations by applying error-controlled smoothening to finite element approximation. Possible benefits of the proposed finite element scheme are discussed and the numerical comparison with the typical adaptive scheme is provided.

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R. H. Drebotiy, H. A. Shynkarenko. 2024-11-19. Quantum-assisted h{\lambda}-adaptive finite element method. https://arxiv.org/abs/2411.12687

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