A posteriori error estimates of two-grid weak Galerkin methods for semilinear elliptic differential equations

• Published in: Applied numerical mathematics Vol. 187; pp. 277 - 294
• Main Authors: Chen, Luoping, Dai, Jiajia, Wen, Yiming
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2023
• Subjects: A posteriori error estimates; Semilinear elliptic differential equations; Two-grid weak Galerkin method; A posteriori error estimates; Semilinear elliptic differential equations; Two-grid weak Galerkin method
• ISSN: 0168-9274
• DOI: 10.1016/j.apnum.2023.02.019

In this paper, we investigate the residual-based a posteriori error estimates of two-grid weak Galerkin (WG) methods for second order semilinear elliptic partial differential equations (PDEs). First, we propose two different two-grid weak Galerkin methods for the model problem and then establish a posteriori error estimators of the two-grid weak Galerkin methods. Theoretical analysis is given to prove the reliability and efficiency of the error estimators. We mainly study the lowest order case of WG element (Pj(T),Pℓ(∂T),RTj(T)) with j=ℓ=0[19]. Numerical experiments are provided to confirm the theoretical results.