{"action":"created","issue":{"url":"https://api.github.com/repos/dealii/dealii/issues/8710","repository_url":"https://api.github.com/repos/dealii/dealii","labels_url":"https://api.github.com/repos/dealii/dealii/issues/8710/labels{/name}","comments_url":"https://api.github.com/repos/dealii/dealii/issues/8710/comments","events_url":"https://api.github.com/repos/dealii/dealii/issues/8710/events","html_url":"https://github.com/dealii/dealii/issues/8710","id":490741696,"node_id":"MDU6SXNzdWU0OTA3NDE2OTY=","number":8710,"title":"Fichera corner Maxwell simulation fails","user":{"login":"dangars","id":25910642,"node_id":"MDQ6VXNlcjI1OTEwNjQy","avatar_url":"https://avatars0.githubusercontent.com/u/25910642?v=4","gravatar_id":"","url":"https://api.github.com/users/dangars","html_url":"https://github.com/dangars","followers_url":"https://api.github.com/users/dangars/followers","following_url":"https://api.github.com/users/dangars/following{/other_user}","gists_url":"https://api.github.com/users/dangars/gists{/gist_id}","starred_url":"https://api.github.com/users/dangars/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/dangars/subscriptions","organizations_url":"https://api.github.com/users/dangars/orgs","repos_url":"https://api.github.com/users/dangars/repos","events_url":"https://api.github.com/users/dangars/events{/privacy}","received_events_url":"https://api.github.com/users/dangars/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":3,"created_at":"2019-09-08T11:16:42Z","updated_at":"2019-09-08T12:47:23Z","closed_at":null,"author_association":"CONTRIBUTOR","body":"@bangerth , @tamiko and @tjhei During the workshop I showed you some Maxwell simulations in which the solution was discontinuous. I've been working on this and I've been able to isolate the problem. I find these discontinuities when I have sharp metallic corners.\r\n\r\nI find the same problem for `Nedelec` and for `NedelecSZ`. I don't know if the problem is related to the finite element. @rosskynch any ideas?\r\n\r\nThe Nedelec element is supposed to be able to deal with the singularities of the Maxwell equations. An example is the Fichera Corner. I found that `deal.II` provides the [Fichera Corner geometry (hyper_L)](https://www.dealii.org/current/doxygen/deal.II/namespaceGridGenerator.html#a3b2a4ad8296c2b72a11d23b5969e8cc0) and there is a reference to Fichera in the `deal.II` documentation, which makes think me that somebody studied these problems with `deal.II` in the past.\r\n\r\nThe test #8709 reproduces the problem. The manufactured solution has a singularity for `curl(curl E)` at `x=y=0`. The solution for `E_z` is correct, but the solution is discontinuous for `E_x` and `E_y`. Below you can find the results for `z=0`:\r\n\r\n![e_z](https://user-images.githubusercontent.com/25910642/64487191-8bae4900-d237-11e9-834d-1b92598afdc9.png)\r\n![e_x](https://user-images.githubusercontent.com/25910642/64487187-7cc79680-d237-11e9-81b9-b01e44a440ac.png)\r\n![e_y](https://user-images.githubusercontent.com/25910642/64487189-851fd180-d237-11e9-9736-1221239157e7.png)\r\n"},"comment":{"url":"https://api.github.com/repos/dealii/dealii/issues/comments/529199424","html_url":"https://github.com/dealii/dealii/issues/8710#issuecomment-529199424","issue_url":"https://api.github.com/repos/dealii/dealii/issues/8710","id":529199424,"node_id":"MDEyOklzc3VlQ29tbWVudDUyOTE5OTQyNA==","user":{"login":"dangars","id":25910642,"node_id":"MDQ6VXNlcjI1OTEwNjQy","avatar_url":"https://avatars0.githubusercontent.com/u/25910642?v=4","gravatar_id":"","url":"https://api.github.com/users/dangars","html_url":"https://github.com/dangars","followers_url":"https://api.github.com/users/dangars/followers","following_url":"https://api.github.com/users/dangars/following{/other_user}","gists_url":"https://api.github.com/users/dangars/gists{/gist_id}","starred_url":"https://api.github.com/users/dangars/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/dangars/subscriptions","organizations_url":"https://api.github.com/users/dangars/orgs","repos_url":"https://api.github.com/users/dangars/repos","events_url":"https://api.github.com/users/dangars/events{/privacy}","received_events_url":"https://api.github.com/users/dangars/received_events","type":"User","site_admin":false},"created_at":"2019-09-08T12:47:23Z","updated_at":"2019-09-08T12:47:23Z","author_association":"CONTRIBUTOR","body":"All my tests with `std::complex` that don't have singularities give good results, but I'll try real algebra.\r\n\r\nI'll try h-refinement with the old element.\r\n\r\nThis is a very basic question: I've been reading Peter Monk book, but it is still not clear to me how the continuity is enforced with the Nedelec element. The electric field should be continuous if there is no dielectric boundary, in fact the condition for the longitudinal continuity of the Electric field  (Monk book): `nu*(epsilon_r1*E_1-epsilon_r2*E_2)=rho_s` with `nu` the normal vector. \r\n\r\nThe nedelec element enforces continuity in the tangential part of the electric field (edge degree of freedom). How does the Nedelec element enforces the continuity of the longitudinal component in the case of no dielectric boundaries? In the test #8709 there are no dielectric boundaries, the material is homogeneous, therefore there shouldn't be any discontinuities in the electric field."}}
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