Convergence analysis of a Petrov-Galerkin method for fractional wave problems with nonsmooth data

TL;DR

This paper investigates the convergence of a Petrov-Galerkin method applied to fractional wave problems with nonsmooth data, establishing well-posedness, regularity, and optimal convergence through theoretical analysis and numerical validation.

Contribution

It provides the first optimal convergence analysis for Petrov-Galerkin methods on fractional wave problems with nonsmooth data.

Findings

Established well-posedness and regularity of solutions.

Proved optimal convergence rates for the numerical method.

Validated theoretical results with numerical experiments.

Abstract

This paper analyzes the convergence of a Petrov-Galerkin method for time fractional wave problems with nonsmooth data. Well-posedness and regularity of the weak solution to the time fractional wave problem are firstly established. Then an optimal convergence analysis with nonsmooth data is derived. Moreover, several numerical experiments are presented to validate the theoretical results.