A Posteriori Error Majorants for FEM Solutions of Plate Bending Problem upon Winkler Subgrade1

• Published in: Numerical analysis and applications Vol. 16; no. 1; pp. 34 - 44
• Main Author: Korneev, V. G.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 2023; Springer Nature B.V
• Subjects: Boundary conditions; Errors; Finite element method; Lower bounds; Mathematics; Mathematics and Statistics; Norms; Numerical Analysis; mixed finite element method; lower error bounds; singularly perturbed elliptic equations of 4th order; a posteriori error bounds
• ISSN: 1995-4239; 1995-4247
• DOI: 10.1134/S1995423923010044

The paper is devoted to the mixed finite element method for the equation  ,  , with boundary conditions   on , where   is the normal to the boundary and   is an arbitrary constant on each finite element. At   residual type a posteriori error bounds for the mixed Ciarlet–Raviart method were derived by several authors at the use of different error norms. The bounds, termed sometimes a posteriori functional error majorants, seem to be less dependent on the constants in the general approximation bounds and are more flexible and adaptable for attaining higher accuracy at practical implementation. In this paper, we present a posteriori functional error majorants for the mixed Ciarlet–Raviart method in the case of   and having large jumps. Robustness and sharpness of the bounds are approved by the lower bounds of local efficiency.