Application of randomized quadrature formulas to the finite element method for elliptic equations
Abstract
The implementation of the finite element method for linear elliptic equations requires to assemble the stiffness matrix and the load vector. In general, the entries of this matrix-vector system are not known explicitly but need to be approximated by quadrature rules. If the coefficient functions of the differential operator or the forcing term are irregular, then standard quadrature formulas, such as the barycentric quadrature rule, may not be reliable. In this paper we investigate the application of two randomized quadrature formulas to the finite element method for such elliptic boundary value problems with irregular coefficient functions. We give a detailed error analysis of these methods, discuss their implementation, and demonstrate their capabilities in several numerical experiments.
Fields of Study & Subjects
Probabilistic and Robust Engineering Design
Advanced Numerical Methods in Computational Mathematics
Matrix Theory and Algorithms
Publication details
- Journal / source
- BIT Numerical Mathematics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 66
- Issue
- 2
- Pages
- 31–31
- Publication date
- 22 April 2026
- Language
- EN