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

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.