  Correlation and smoothness are terms used to describe a wide variety of
random quantities. In time, space, and many other domains, they both imply the
same idea: quantities that occur closer together are more similar than those
further apart. Two popular statistical models that represent this idea are
basis-penalty smoothers (Wood, 2017) and stochastic partial differential
equations (SPDE) (Lindgren et al., 2011). In this paper, we discuss how the
SPDE can be interpreted as a smoothing penalty and can be fitted using the R
package mgcv, allowing practitioners with existing knowledge of smoothing
penalties to better understand the implementation and theory behind the SPDE
approach.

Methodology