A reduced finite element formulation for space fractional partial differential equation

TL;DR

This paper introduces a reduced finite element method for space fractional PDEs using proper orthogonal decomposition, significantly decreasing computational complexity while maintaining accuracy, supported by stability analysis and numerical validation.

Contribution

It presents a novel reduced FE formulation for space fractional PDEs via proper orthogonal decomposition, with stability and error analysis, and numerical verification.

Findings

Reduced FE model decreases computational complexity

Stability and error estimates are established

Numerical experiments confirm effectiveness

Abstract

Applying proper orthogonal decomposition to a usual finite element (FE) formulation for space fractional partial differential equation, we get a reduced FE model, which greatly reduces the complexity of computation. Then, the stability analysis and error estimate for the reduced model are presented. Finally, we verify the effectiveness of the algorithm by numerical experiments.