Normally, the approach to answering such a question would be to turn to measurements of the phenomenon; but in the case of sea level rise, there is a major problem in that tide gauge stations rise or fall as the land they sit upon rises or falls, thereby confounding the data. In addition, newer satellite measurements do not extend very far back in time. Thus, the method adopted in this study attempts to overcome these two issues.
Wenzel and Schroter use neural nets for infilling of missing data at individual stations and for estimating weights for individual gauges. They found 56 stations with at least 50 years of data; and they adjusted them before use by correcting for land movement (up or down). The training data for the neural net were three sets of altimetry data for recent decades, and all three results were shown. By basin, they indicated no net trend for the South Atlantic and tropical Indian Oceans, and a net decline in sea level for the Southern Indian Ocean. The Pacific Ocean showed an approximate 70-year oscillation in sea level that correlates (with lag) with the Pacific Decadal Oscillation (PDO), while the Atlantic showed cycles of 23 and 65 years. Overall, ocean basin changes showed correlations with the PDO and Southern Annular Mode indices, with lags; and Wenzel and Schroter say this shows -- along with the clear annual cycles in sea level -- that their final result correctly reflects the effects of water temperature on sea level.
For the globe as a whole, the two researchers found a linear upward sea level trend of 1.56 mm/year, with no sign of acceleration in recent decades. This result is about one-half of the value used by the IPCC; and if continued, it would produce one-half foot of sea level rise over the next 100 years. These results thus agree with those of Hagedoorn et al. (2007) of 1.46 mm/year and Woppelmann et al. (2009) of 1.61 mm/year, as well as several other recent studies that give only slightly higher values around 1.7-1.8 mm/year.
In summation, it would thus appear that careful analyses of tide gauge records by multiple teams does not show the rapid sea level rise proposed by the IPCC; and they also do not show any acceleration of sea level rise.