A posteriori error analysis for a continuous space-time finite element method for a hyperbolic integro-differential equation

TL;DR

This paper develops a posteriori error estimates for a continuous space-time finite element method applied to hyperbolic integro-differential equations, enabling adaptive strategies for improved accuracy.

Contribution

It introduces new a posteriori error representations and estimates tailored for a space-time finite element approach to hyperbolic integro-differential equations, facilitating adaptive computation.

Findings

Error representations based on space-time cells

A posteriori error estimates using weighted projections

Framework for adaptive strategies in hyperbolic integro-differential equations

Abstract

An integro-differential equation of hyperbolic type, with mixed boundary conditions, is considered. A continuous space-time finite element method of degree one is formulated. A posteriori error representations based on space-time cells is presented such that it can be used for adaptive strategies based on dual weighted residual methods. A posteriori error estimates based on weighted global projections and local projections are also proved.