Web spline error estimation of non-cooperative elliptic equations for population dynamics

TL;DR

This paper investigates the error estimation of the WEB-S finite element method applied to non-cooperative elliptic systems with mixed boundary conditions, providing computable bounds and guiding mesh refinement through a posteriori error estimates.

Contribution

It introduces a novel error analysis framework for WEB-S finite element method on complex elliptic systems with mixed boundary conditions, supported by regularity analysis and numerical validation.

Findings

Derivation of computable a posteriori error bounds

Identification of error zones for mesh refinement

Numerical experiments confirming theoretical results

Abstract

We analyze the error of the WEB-S finite element method applied to elliptic systems with non-cooperative dominant coupling,with a mixed Dirichlet/Neumann/Robin boundary condition. This problem is strongly related to a posteriori error estimates, giving computable bounds for computational errors and detecting zones in the solution domain where such errors are too large and certain mesh refinements should be performed. These results are based on an extensive regularity analysis of the interface problems of concern.Finally, the error analysis is illustrated by numerical experiments.