The content starts by introducing the convection-diffusion-reaction equation and the challenges in numerically approximating its solution, particularly in the presence of layers. It then discusses the recently proposed algebraic stabilization schemes, including the Symmetric Monotone Upwind-type Algebraically Stabilized (SMUAS) method, which satisfies the discrete maximum principle on arbitrary simplicial meshes.
The main focus of the work is on developing residual-based a posteriori error estimators for the algebraic stabilization schemes, extending the analysis previously done for algebraic flux correction schemes. The derivation of the global upper bound for the error in the energy norm is presented, along with the discussion of the local lower bound.
Numerical studies are then provided, comparing the performance of the SMUAS method with the algebraic flux correction scheme using the BJK limiter. The results show that both methods achieve optimal convergence rates, but the SMUAS method is significantly more efficient in terms of the number of nonlinear iterations and rejections required to solve the system of equations.
The paper concludes by summarizing the key findings and highlighting the potential for further numerical studies of the different algebraic stabilization schemes on adaptively refined grids.
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arxiv.org
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by Abhinav Jha kl. arxiv.org 04-04-2024
https://arxiv.org/pdf/2404.02804.pdfDybere Forespørgsler