A posteriori error analysis for a continuous space-time finite element method for a hyperbolic integro-differential equation
This work provides rigorous error analysis for numerical methods in a specific class of hyperbolic integro-differential equations, which is an incremental contribution to the field of numerical analysis.
The authors develop a posteriori error analysis for a continuous space-time finite element method applied to a hyperbolic integro-differential equation, providing error representations and estimates suitable for adaptive mesh refinement.
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.