Quantum-assisted h{\lambda}-adaptive finite element method
Numerical Analysis
2024-11-20 v1 Numerical Analysis
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.
Cite
@article{arxiv.2411.12687,
title = {Quantum-assisted h{\lambda}-adaptive finite element method},
author = {R. H. Drebotiy and H. A. Shynkarenko},
journal= {arXiv preprint arXiv:2411.12687},
year = {2024}
}