I found a rather interesting essay on the Harry Potter Wiki, written by the user Acrobasis01, which in my opinion is well-researched enough to be canon. Read for yourself:

Rowling gives enough information in Goblet of Fire and in a statement to fans at a reading at a cancer care center in Glasgow to locate Durmstrang in a specific country and possibly in a specific region of that country. She gives 10 very specific clues.

1. In the "far north." (Rowling 2000, 23:417)

2. Access to the sea. (Rowling 2000, 15:246)

3. Must predate 1294. (Rowling 2000, 12:187)

4. Castle has only "four floors". (Rowling 2000, 23:417)

5. Few hours of daylight in winter. (Rowling 2000, 23:417)

6. Extensive grounds. (Rowling 2000, 23:417)

7. Mountains. (Rowling 2000, 23:417)

8. Lakes. (Rowling 2000, 23:417)

9. Forests. (Rowling 2000, 23:417)

10. "Somewhere in Scandinavia (Scruton 2000: Rowling Quote)

If Durmstrang, a gross corruption of the German "Sturm und Drang" (Storm and Stress), lies to the "far north" of Hogwarts, then it may logically be located in only one of six geographic locations: the Shetland Islands, UK; the Faroe Islands, Norway, Sweden, Finland and Russia (Kaufmann et al. 2004, Britain Ireland Castles 2013). Further, in Goblet of Fire, Rowling describes it as being in the "far north" where the school receives only a few hours of daylight during the winter (Rowling 2000, Scruton 2000).

Of the six locations, only Norway has castles in the "far north" that best match Rowling's description of the castle that houses the Durmstrang Institute of Magic (Scruton 2000).

The castles of the Shetland Islands are little more than large fortified houses or, in the case of the 19th century Balfour Castle, a stylized mansion. All of them, Muness on the Isle of Unst, Scalloway on Shetland Island, and Balfour on Shapinsay, are too small to house more than a handful of students. Even if disguised by magic, all of the castles date from years too late to satisfy Rowling's date of 1294 (Rowling 2000,Turner 1998, McMillan 2008, Britain Ireland Castles 2013). And the islands are too small to provide the miles upon miles of "extensive grounds" with "mountains and lakes" described by Rowling in Goblet of Fire (Rowling 2000). In fact the islands have no mountains at all, nor any prospect of "winter sports" such as skiing (Turner 1998, Rowling 2000, McMillan 2008, Shetland 2013).

Medieval castle building in the Scandinavian countries followed a completely different tradition and pattern than it did in Britain, France, Switzerland, Germany, the Baltic States and Eastern Europe from Poland to Bulgaria. Governments in Scandinavia were more centralized and controlled larger regions. Local nobles were far less independent and had to request permission for the national king to build even an unfortified manor house. Castles, on the other hand, were fortresses built by kings and Roman Catholic bishops under the king's direction to fortify harbors or borders with neighboring states. These were unlike the private castles of nobles in countries further south, who exercised a good deal more independence than those in medieval Scandinavia. Feudalism followed a different pattern in Scandinavia. So the castles there were not the residences of nobles, but were instead military garrisons of the national government (Kaufmann et al. 2004).

The Faroe Islands (Faroese: Føroyar), are a self-governing country within the Kingdom of Denmark, situated mid way between Norway and Iceland at a latitude of 62°N. The only stone structure of significant size on any of the Faroe Islands was the Magnus Cathedral of the ancient Roman Catholic Diocese in the village of Kirkjubøur on the island of Streymoy (Streymoy 2013, Magnus Cathedral 2013). The small fishing and agricultural communities did not need fortifications.

One may consider the ruined church because the island of Streymoy is mountainous with many lakes described by Rowling in Goblet of Fire (Rowling 2000) and the cathedral dates to within six years of the 1294 date for the existence of Durmstrang. However, the Cathedral was built by Bishop Erlendur of Bergen in 1300 and lacks the fortifications and battlements implied in Goblet of Fire that would make it a castle (Kaufmann et al. 2004). This not only makes it six years too late in time for it to house Durmstrang (Rowling 2000), but it also completely rules it out on account of the Scandinavian Church's lethal hostility to witchcraft in the 11th to 14th centuries (Sturlusson 1230, Carlyle 1875, Lagerqvist and Åberg 2002, Mitchell 2011).

Swedes have been building fortifications for close to two thousand years. However, the Swedes did not build castles in the far north of Sweden proper. All of Sweden's castles are in the south, usually at the entrance to harbors or rivers, or on lakes that were key points on northern trade routes (Castles in Sweden 2013). The icy plains of northern Sweden did not need fortifications. Sweden was an aggressive, expansionist country and only built castles in conquered territories, such as Finland (Lagerqvist & Åberg 2002, Kaufmann et al. 2004, Castles in Sweden 2013).

Sweden's northernmost castles are less than 1.5 degrees (87 miles) north of the latitude Rowling has described for Hogwarts and would be regarded as more east than "far north." The Swedish kings, with good justification, did not regard the far north, which was home to Sami reindeer herders and not much else, as presenting much of a threat to the kingdom. The arctic winter was their best defense (Lagerqvist & Åberg 2002, Kaufmann et al. 2004, SpottingHistory 2013, Castles in Sweden 2013).

When Sweden conquered the lands to the east, they built castles further north in Finland to guard against invasion from the Novogorod Republic, a state extending from the northern part of European Russia to the Arctic Ocean. Therefore, the northernmost castles built by the Swedish kings are now in Finland. However, even though all of the Finnish castles are far enough north, they date to a period later than Rowling's date for the first Triwizard tournament, 1294. So Finland has to be ruled out (Lagerqvist & Åberg 2002, Kaufmann et al. 2004, Castles in Finland 2013).

Russia must be ruled out also. The Russians of the Novogorod Republic or the principalities and duchies further south did not build castles. They built kremlins, huge fortified complexes in the center of cities. In western Europe, armies were small. Countries were small. So castles would do. In Russia, everything was on a scale so vast that western Europeans have never been able to grasp the size. Russians built fortifications large enough to house entire armies or the population of a city or town. They were designed to hold off invaders long enough for the Russian winter to destroy a besieging army. And the armies the Russians faced also were on a scale to match the country and its fortifications. Vast hordes of steppe dwellers were the principal threat. So castles were simply be too small to keep out an army of 100,000 to a million or more (Kaufmann et al. 2004, Castles in Russia 2013).

In 1293, the Golden Horde swept out of the Steppes of Central Asia with an army of more than a million Mongol horse soldiers. They easily conquered the Principalities of Moscow, Belarus and Bulgaria, where stone castles and fortifications of wood and earth were overwhelmed in a matter of days. The huge kremlins of the Novogorod Republic withstood the invaders until the winter of northern Russia forced them out. Further, most of the kremlins and huge fortified monasteries constructed in the far north of Novogorod also date to a period much later than 1294. So Russia can be ruled out as a possible location for Durmstrang (Kaufmann et al. 2004, Castles in Russia 2013).

All that is left is the northern region of Norway where castles are old enough to predate the 1294 date for the first Triwizard tournament (Rowling 2000, Scruton 2000, Kaufmann et al. 2004).

Most of the castles in Norway were built between the end of the 10th century (1100s) and the beginning of the 13th (1400s). The earliest castles were coastal, guarding harbor towns. The later castles were border fortifications, guarding the frontier against the Swedes and Russians of Novogorod. The earliest of the border castles were built in the far north between 1263 and 1280 by Norwegian King Magnús Hákonarson (now Magnus Håkonsson), also known as Magnús lagabœtir (now Magnus VI Lagabøte or "Magnus the law-mender" (Lagerqvist & Åberg 2002).

Between 1263 and 1280, Magnus VI of Norway constructed a chain of castle fortresses along the Swedish border. They stretched from the Barents Sea to the Skagerrak Strait separating Denmark and Norway. He began in the far north, starting with Varghøya and Østervågen on the far northern coast of Finnmark. Construction of others further south followed. The last of these fortifications, Vardøhus, was finished by Magnus IV's successors around 1303 (Lagerqvist & Åberg 2002, List 2012, Hill 2013, Vardøhus 2013).

Low, stark and windowless with massive walls, the fortress castles of subarctic and high arctic Norway were austere and built to endure the cold. The northern castles were grim, ugly and forbidding structures, showing few signs of artistic attempts in their architecture. Their, fat, round towers reach four or five stories and fit the description in Goblet of Fire. All had extensive grounds. Only six of these castles are known to have survived. Two are still occupied by the Norwtegian armed forces (List 2012, Hill 2013, Castles in Norway 2013).

The castle furthest north, Vardøhus, once on the border with Novogorod and now near the border with Russia, is presently occupied by troops of the Norwegian army. The rest are in ruins and exist in various stages of disrepair from generally intact but roofless structures, such as Steinvikholm Castle and Kalø Stronghold, or exist as little more than jumbles of toppled stones, such as Hammarhus Fortress (destroyed by Swedes in 1570). Others have vanished entirely like Varghøya and Østervågen. Many are simply nameless piles of overgrown stones that still retain the shape of the original structure (Stagg 1952, Kavli 1987, List 2012, Hill 2013, Castles in Norway 2013, Vardøhus 2013).

One of the vanished castles was in a mountain valley at the entrance to the Daltröll Pass in the Lyngen Fjell mountain range (named for the lingonberries, Vaccinium vitis-idaea, that grow there. The castle, called Størmarogstreita in Old Norse, is some distance southeast of Tromsø, in the county of Troms, Norway. The castle was on an island in a small, shallow, glacial lake somewhere in the mountains beyond the terminus of Spøkelsefjord (Nor. Spøkelsefjorden, "Ghost Fjord"). It was a long, narrow fjord with a nearly hidden entrance, branching off from either Balsfjorden (Rune Master's Fjord), Storfjorden (Big Fjord) or Lyngenfjorden (Lingonberry Fjord). A small fishing village called Spøkelsefjordbotn (Ghost Fjord Bottom) near the terminus of the fjord was a source of supply for the fortress (Vickers 1885, Cooper 1914,Stagg 1952, Kavli 1987, Hill 2013).

Both the village and the fjord have apparently vanished or now go by other names (Vickers 1885, Cooper 1914). Several of the far northern castle fortresses, including Østervågen, Størmarogstreita and Varghøya, also have vanished without a trace. Abandoned for more than 600 years, they may now be little more than mounds of moss and grass with carved stones breaking the surface here and there (Stagg 1952, Kavli 1987, Vardøhus 2013).

The location associated with Spøkelsefjord and the castle of Størmarogstreita appears to be the best candidate for Rowling's Durmstrang. This region of northern Norway satisfies all ten of the characteristics of Durmstrang that Rowling describes for the location of the castle and school: (1) Scandinavia (Scruton 2000), (2) "far north", (3) low (4-story) castle, (4) built before 1294, (5) "few hours of daylight, (6) extensive grounds, (7) mountains all around, (8) forests, (9) lakes, (10) access to the sea (Rowling 2000).

1. Rowling's statement in Glasgow at Maggie's Cancer Caring Centre that "Durmstrang is somewhere in Scandinavia - in the far north of Sweden or Norway" (Scruton 2000). In Goblet of Fire (Rowling 2000,  23:417) "far north" is described by the effects of winter and its short days. It appears to be far enough north of Hogwarts that it would difficult, uncomfortable or impossible to reach by flying on a broom, apparating, traveling by port key or by the floo network, making travel by magical ship necessary (Rowling 2000, 15:246). Maybe it would be someplace that would take at least a day or two to reach by train or ship, at least 200 miles. That is, 200 miles north of Hogwarts, which would place it across the north sea in Scandinavia.

2.  Year of construction must be before 1294, the year of the first Triwizard tournament (Rowling 2000, 12:187). All of the castles in the far north of Norway were built in the 1200s except Vardøhus, which was begun in the 1280s and competed in 1306. The rest predate the Triwizard tournament by several to many years (Castles in Norway 2013, Hill 2013).

3. Castle is "four stories high". Norwegian medieval castles are low, thick-walled fortresses. Those in the far north are largely windowless. They were designed to withstand short sieges by small Swedish forces. If the castle could hold out for three or four months, the arctic winter would then take over. The garrison in the fortress would be protected from the elements while the winter would either drive out the invaders or destroy them. In the far north, winter was the best defense (List of Castles in Norway 2013).

4. Short daylight in winter. What is meant by "few hours"?  4 or 5 hours of twilight (68ºN-70ºN), 3-6 hours sun (63ºN-67ºN). The castles in northern Norway have very short days. The only surviving one, Vardøhus, is north of the Arctic Circle and does not see the sun rise for nearly two months. However, it does have daylight in the form of civil twilight, which lasts for around four hours on the shortest days of the year. Any castle north of Trondheim, particularly in the Counties of Troms and Finnmark would qualify as a possible location for Durmstrang's "few hours of daylight" (US Naval Observatory 2013).

6. Extensive grounds. All the fortresses and outposts north of Trondheim have extensive open lands surrounding them, mostly forests and grassy mountain valleys (Hill 2013).

7. Mountains. Norway is the most mountainous country in Scandinavia. Mountain ranges in the Scandinavian chain run the full length of the country. In the far north latitudes, the Lyngen Fjell mountains are among the most impressive mountains in the county of Troms. Several areas have extensive winter recreational areas for skiing (Heidar 2001, Kagda & Cooke 2006, Harding et al. 2007).

8. Forests. Northern limit of the Boreal forest is the 10º summer isotherm (69.2ºN at 1,500 ft) to 70ºN at low elev). The warming effect of the Gulf Stream allows the northern boreal forest or taiga to grow further north than other locations. Further east in Sweden, Finland and Russia the tree line is much further south. In the far north in those locations there is grassland and tundra. However, in Norway, forests grow in lower elevations further north than anywhere else in Europe (Heidar 2001, Kagda & Cooke 2006, Harding et al. 2007). Again the region of Troms County has sufficient forested lands at lower elevations to qualify as a location of Durmstrang.

9. Lakes. Many in Lyngen Fjell region. The mountains of northern Norway and Sweden are filled with thousands of lakes. Some estimates suggest that there are more than 400,000 lakes in northern Norway (Heidar 2001, Kagda & Cooke 2006, Harding et al. 2007).

10. Access to the sea. Fjords in Norway provide excellent access to the sea. The Gulf Stream's warming effect also keeps many of the fjords open throughout the winter. At Vardø on Norway's coast with the Barents Sea, the sea does not freeze but stays open year round (Vickers 1885, Cooper 1914).


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