Resolutiondependence

Resolutiondependence is the phenomenon in which the outcome of a computation, simulation, or measurement changes with the resolution at which the problem is represented or sampled. It arises when discretization or sampling introduces errors that affect results, and these errors may vary in magnitude and character as the resolution is altered.

This dependence is common in numerical simulations of physical systems, such as solving partial differential equations with finite difference or finite element methods. Discretization error, aliasing, and boundary-condition representation can cause quantities of interest to converge only slowly or to different limiting values if the grid spacing, time step, or basis functions are not chosen appropriately. In computational fluid dynamics, for example, insufficient resolution can misrepresent turbulence and transport phenomena.

Resolutiondependence also appears in imaging and computer graphics, where sampling and rendering decisions determine visible details, shading, and artifacts. In data analysis, binning, resampling, or choosing a time or spatial scale can alter statistical estimates, leading to scale-dependent conclusions.

Assessing resolutiondependence typically involves grid or parameter refinement studies. By comparing results at multiple resolutions and measuring error norms against a reference solution or between successive refinements, one can estimate convergence rates and identify when results become insensitive to further resolution increases. Mitigation strategies include adaptive mesh refinement, multiscale or subgrid models, oversampling where feasible, and reporting the effective resolution and uncertainty alongside results. Well-documented resolution studies enhance reproducibility and reliability of conclusions.