Normally in the graduation of adjectives one element of a group is compared to another element of the group or to all members of the group.
positive: Maria is tall.
comparative: John is taller than Maria.
superlative: Eric is the tallest of all.
The term elative however refers to a graduation where there is no comparision. It is a superlative that does not compare one element to all other elements of the group, "He has the fastest car of all", but expresses only a high intensity of a property, "He is the greatest". However it can be questioned whether that is really an elative that can be compared to an elative in roman languages. In a sentence like "He is the greatest" the "of all" is implicetly present. He is the greatest doesn't correspond to "He is very great". The sentence "He is very great" describes indeed only a high quality of something without any comparison.
In English the comparative and the superlative can be formed in two different ways, but both forms are used the same way. How the comparative is formed depends on the amount of syllables. The meaning is the same. In the case that the adjective / adverbe has only one syllable we add -er, -est, in the case that the adjective / adverb has several syllables, the comparative is formed with more + adjective / adverb, the superlative with most + adjective / adverbe.
This car is big and that car is bigger, but the car that is parked there ist the biggest of all.
This woman is beautiful and that woman is more beautiful, but the woman who is dancing is the most beautiful of all.
Both forms, biggest and most beautiful, have the same function. To keep it short and simple: There is no elative in English. The situation in the roman languages is completely different. We can form a comparative of any adjectives or adverb following the scheme mais + adjective / adverb and the superlative with o mais + adjective / adverb de, see 21.2, and in parallel there is a form with -issimo, that can be formed as well with any adjective / adverb, but has a completely different meaning. The last form describes a high intensity of a property and doesn't compare.
Rodrigo é o mais preguiçoso de todos os alunos.
=> Rodrigo is the laziest students of all.
Rodrigo é preguiçosissimo.
=> Rodrigo is very lazy.
It is useful to see this difference. In English there are two different ways to form the superlative, but these two forms don't differ in the meaning. Whether we use one form or the other depends on the structure of the adjective / adverbe. In Portuguese the superlative of any verbe / adjective can be formed in two different ways, but the meaning is not the same. If it is formed with the scheme (o) mais + adjective / adverbe one element is compared to all other elements of the group. If it is formed with -issimo there is no comparison at all. In this case it describes just the intensity of something and is called elative. There is no difference in meaning between amaríssimo (bitterest) and muito amargo (very bitter).
The elative of many adjectives / adverbes is rarely used.
For regular adjectives / adverbs the building of the elative is simple. The final o, if there is one, is left out and two what is left the ending -issimo, -issima, íssimos, -issimas is added. The adjective has to agree in gender and number with the noun it refers to: um homem feliccísimo <=> uma mulhier felicíssima, uns homens felicíssimos <=> umas mulheres felicíssimas.
belo - belíssimo
nice - very nice (nicest)
cheio - cheíssimo
full - very full (fullest)
estranho - estranhíssimo
strange - very strange (strangest)
feio - feíssimo
ugly - very ugliy (ugliest)
feliz - felicíssimo
happy - very happy (happiest)
límpio - limpiíssimo
clean - very clean (cleaniest)
normal - normalíssimo
normal - very normal
In addition there are a big number of irregular elatives, but there is no real need to know them.
amável - amabilíssimo
kind very kind (kindest)
alto - supremo
highe very high (highest)
amargo - amaríssimo
bitter very bitter (bitterest)
feliz - felicíssimo
happy very happy (happiest)
feroz - ferocíssimo
wild very wild (wildest)
fiel - fidelíssimo
loyal very loyal (loyalest)
frio - frigidíssimo
cold very cold (coldest)
grande - máximo
big very big (biggest)
jovem - juveníssimo
young very young (youngest)
preguiçoso - pigérrimo
lazy very lazy (laziest)
sábio - sapientíssimo
wise very wise (wisest)
senil - senilíssimo
senile very senile (senilest)
simples - simplíssimo
simple very simple (simplest)
veloz - velocíssimo
fast very fast (fastest)
In English the "elative" is used when the adjective has only one syllable, the formation with more is not an alternative.
Mary is nicer that Joanna. <=> ~ Mary is more nice than Joanna.
In Portuguese it is not an alternative for the normal superlative, it is a different form with a different meaning.
This author would say that the "elative" in English in normally not possible.
João mostrou-se um amigo fidelíssimo.
João proved to be a very loyal friend.*
A população daquele país é paupérrima.
The population of this country is very poor. **
* not: João proved to be a loyalist friend.
** not: The population of this country is poorest.
Since the elative has no semantical value on its own, in other words there is no difference between this form and the analytical form, in the examples above we could have written instead of fidelíssimo as well muito fiel, instead of paupérrima we could have written as well muito pobre and is only a special grammatical form. Many grammars designate a combination of an adverb expressing high intensity (extraordinariamente, muito, etc.) and an adjective as an elative.
Paulo é extraordinariamente atencioso.
Paulo is extraordinarily attentive.
The author would say, that this is nonsense. If we start to create new grammar terms for combination of adverb and adjective we get an endless number of terms.