Implement polynomial and Lagrange degrees for elements (#275)

* changes

* Adding degree functions

* degress of more elements

* implement more degrees

* ruff

* more degrees

* transition degrees

* ruff

* typing

* update some last_updated

* fixes

* ruff

CHANGELOG_SINCE_LAST_VERSION.md

@@ -1 +1,2 @@
 - Corrected polyset for Arnold-Winther element
+- Added sub- and superdegree functions

demo/custom_element.py

@@ -40,6 +40,7 @@ def __init__(self, reference, order):
     min_order = 1
     max_order = 1
     continuity = "L2"
+    value_type = "scalar"
     mapping = "identity"
 
 

symfem/elements/abf.py

@@ -77,8 +77,25 @@ def init_kwargs(self) -> typing.Dict[str, typing.Any]:
         """
         return {"variant": self.variant}
 
+    @property
+    def lagrange_subdegree(self) -> int:
+        return self.order
+
+    @property
+    def lagrange_superdegree(self) -> typing.Optional[int]:
+        return self.order + 2
+
+    @property
+    def polynomial_subdegree(self) -> int:
+        return self.order
+
+    @property
+    def polynomial_superdegree(self) -> typing.Optional[int]:
+        return self.order * 2 + 2
+
     names = ["Arnold-Boffi-Falk", "ABF"]
     references = ["quadrilateral"]
     min_order = 0
     continuity = "H(div)"
+    value_type = "vector"
     last_updated = "2023.06"

symfem/elements/ac.py

@@ -75,8 +75,28 @@ def init_kwargs(self) -> typing.Dict[str, typing.Any]:
         """
         return {"variant": self.variant}
 
+    @property
+    def lagrange_subdegree(self) -> int:
+        if self.order < 2:
+            return self.order
+        else:
+            return self.order // 2
+
+    @property
+    def lagrange_superdegree(self) -> typing.Optional[int]:
+        return self.order + 1
+
+    @property
+    def polynomial_subdegree(self) -> int:
+        return self.order
+
+    @property
+    def polynomial_superdegree(self) -> typing.Optional[int]:
+        return self.order + 1
+
     names = ["Arbogast-Correa", "AC", "AC full", "Arbogast-Correa full"]
     references = ["quadrilateral"]
     min_order = 0
     continuity = "H(div)"
+    value_type = "vector"
     last_updated = "2023.06"

symfem/elements/alfeld_sorokina.py

@@ -125,9 +125,26 @@ def __init__(self, reference: Reference, order: int):
 
         super().__init__(reference, order, poly, dofs, reference.tdim, 1)
 
+    @property
+    def lagrange_subdegree(self) -> int:
+        raise NotImplementedError()
+
+    @property
+    def lagrange_superdegree(self) -> typing.Optional[int]:
+        raise NotImplementedError()
+
+    @property
+    def polynomial_subdegree(self) -> int:
+        raise NotImplementedError()
+
+    @property
+    def polynomial_superdegree(self) -> typing.Optional[int]:
+        raise NotImplementedError()
+
     names = ["Alfeld-Sorokina", "AS"]
     references = ["triangle"]
     min_order = 2
     max_order = 2
     continuity = "C0"
+    value_type = "scalar macro"
     last_updated = "2023.05"

symfem/elements/argyris.py

@@ -64,9 +64,26 @@ def __init__(self, reference: Reference, order: int):
 
         super().__init__(reference, order, poly, dofs, reference.tdim, 1)
 
+    @property
+    def lagrange_subdegree(self) -> int:
+        return self.order
+
+    @property
+    def lagrange_superdegree(self) -> typing.Optional[int]:
+        return self.order
+
+    @property
+    def polynomial_subdegree(self) -> int:
+        return self.order
+
+    @property
+    def polynomial_superdegree(self) -> typing.Optional[int]:
+        return self.order
+
     names = ["Argyris"]
     references = ["triangle"]
     min_order = 5
     max_order = 5
     continuity = "L2"
+    value_type = "scalar"
     last_updated = "2023.05"

symfem/elements/aw.py

@@ -132,10 +132,27 @@ def init_kwargs(self) -> typing.Dict[str, typing.Any]:
         """
         return {"variant": self.variant}
 
+    @property
+    def lagrange_subdegree(self) -> int:
+        return self.order - 1
+
+    @property
+    def lagrange_superdegree(self) -> typing.Optional[int]:
+        return self.order
+
+    @property
+    def polynomial_subdegree(self) -> int:
+        return self.order - 1
+
+    @property
+    def polynomial_superdegree(self) -> typing.Optional[int]:
+        return self.order
+
     names = ["Arnold-Winther", "AW", "conforming Arnold-Winther"]
     references = ["triangle"]
     min_order = 3
     continuity = "integral inner H(div)"
+    value_type = "symmetric matrix"
     last_updated = "2024.09"
 
 
@@ -216,9 +233,26 @@ def init_kwargs(self) -> typing.Dict[str, typing.Any]:
         """
         return {"variant": self.variant}
 
+    @property
+    def lagrange_subdegree(self) -> int:
+        return self.order - 1
+
+    @property
+    def lagrange_superdegree(self) -> typing.Optional[int]:
+        return self.order
+
+    @property
+    def polynomial_subdegree(self) -> int:
+        return self.order - 1
+
+    @property
+    def polynomial_superdegree(self) -> typing.Optional[int]:
+        return self.order
+
     names = ["nonconforming Arnold-Winther", "nonconforming AW"]
     references = ["triangle"]
     min_order = 2
     max_order = 2
     continuity = "integral inner H(div)"
+    value_type = "symmetric matrix"
     last_updated = "2023.06"

symfem/elements/bddm.py → symfem/elements/bddf.py

@@ -78,8 +78,25 @@ def init_kwargs(self) -> typing.Dict[str, typing.Any]:
         """
         return {"variant": self.variant}
 
+    @property
+    def lagrange_subdegree(self) -> int:
+        return self.order // 3
+
+    @property
+    def lagrange_superdegree(self) -> typing.Optional[int]:
+        return self.order + 1
+
+    @property
+    def polynomial_subdegree(self) -> int:
+        return self.order
+
+    @property
+    def polynomial_superdegree(self) -> typing.Optional[int]:
+        return self.order + 1
+
     names = ["Brezzi-Douglas-Duran-Fortin", "BDDF"]
     references = ["hexahedron"]
     min_order = 1
     continuity = "H(div)"
+    value_type = "vector"
     last_updated = "2023.06"

symfem/elements/bdfm.py

@@ -97,8 +97,28 @@ def init_kwargs(self) -> typing.Dict[str, typing.Any]:
         """
         return {"variant": self.variant}
 
+    @property
+    def lagrange_subdegree(self) -> int:
+        if self.reference.name in ["triangle", "tetrahedron"]:
+            return self.order - 1
+        else:
+            return self.order // self.reference.tdim
+
+    @property
+    def lagrange_superdegree(self) -> typing.Optional[int]:
+        return self.order
+
+    @property
+    def polynomial_subdegree(self) -> int:
+        return self.order - 1
+
+    @property
+    def polynomial_superdegree(self) -> typing.Optional[int]:
+        return self.order
+
     names = ["Brezzi-Douglas-Fortin-Marini", "BDFM"]
     references = ["triangle", "quadrilateral", "hexahedron", "tetrahedron"]
     min_order = 1
     continuity = "H(div)"
+    value_type = "vector"
     last_updated = "2023.06"

symfem/elements/bdm.py

@@ -52,8 +52,25 @@ def init_kwargs(self) -> typing.Dict[str, typing.Any]:
         """
         return {"variant": self.variant}
 
+    @property
+    def lagrange_subdegree(self) -> int:
+        return self.order
+
+    @property
+    def lagrange_superdegree(self) -> typing.Optional[int]:
+        return self.order
+
+    @property
+    def polynomial_subdegree(self) -> int:
+        return self.order
+
+    @property
+    def polynomial_superdegree(self) -> typing.Optional[int]:
+        return self.order
+
     names = ["Brezzi-Douglas-Marini", "BDM", "N2div"]
     references = ["triangle", "tetrahedron"]
     min_order = 1
     continuity = "H(div)"
+    value_type = "vector"
     last_updated = "2023.06"

symfem/elements/bell.py

@@ -54,9 +54,26 @@ def init_kwargs(self) -> typing.Dict[str, typing.Any]:
         """
         return {"variant": self.variant}
 
+    @property
+    def lagrange_subdegree(self) -> int:
+        return 4
+
+    @property
+    def lagrange_superdegree(self) -> typing.Optional[int]:
+        return 5
+
+    @property
+    def polynomial_subdegree(self) -> int:
+        return 4
+
+    @property
+    def polynomial_superdegree(self) -> typing.Optional[int]:
+        return 5
+
     names = ["Bell"]
     references = ["triangle"]
     min_order = 5
     max_order = 5
     continuity = "C1"
+    value_type = "scalar"
     last_updated = "2023.05"

symfem/elements/bernardi_raugel.py

@@ -115,12 +115,28 @@ def __init__(self, reference: Reference, order: int):
                         reference, x[i], p.dofs[0], entity=(3, 0), mapping="contravariant"
                     )
                 )
-
         super().__init__(reference, order, poly, dofs, reference.tdim, reference.tdim)
 
+    @property
+    def lagrange_subdegree(self) -> int:
+        return self.order
+
+    @property
+    def lagrange_superdegree(self) -> typing.Optional[int]:
+        return self.order + self.reference.tdim - 1
+
+    @property
+    def polynomial_subdegree(self) -> int:
+        return self.order
+
+    @property
+    def polynomial_superdegree(self) -> typing.Optional[int]:
+        return self.order + self.reference.tdim - 1
+
     names = ["Bernardi-Raugel"]
     references = ["triangle", "tetrahedron"]
     min_order = 1
     max_order = {"triangle": 1, "tetrahedron": 2}
     continuity = "H(div)"
+    value_type = "vector"
     last_updated = "2023.06"

symfem/elements/bernstein.py

@@ -234,8 +234,25 @@ def index(x: int, y: int = 0, z: int = 0) -> int:
 
         super().__init__(reference, order, poly, dofs, reference.tdim, 1)
 
+    @property
+    def lagrange_subdegree(self) -> int:
+        return self.order
+
+    @property
+    def lagrange_superdegree(self) -> typing.Optional[int]:
+        return self.order
+
+    @property
+    def polynomial_subdegree(self) -> int:
+        return self.order
+
+    @property
+    def polynomial_superdegree(self) -> typing.Optional[int]:
+        return self.order
+
     names = ["Bernstein", "Bernstein-Bezier"]
     references = ["interval", "triangle", "tetrahedron"]
     min_order = 0
     continuity = "C0"
+    value_type = "scalar"
     last_updated = "2023.05"

symfem/elements/bfs.py

@@ -50,10 +50,27 @@ def __init__(self, reference: Reference, order: int):
         poly += quolynomial_set_1d(reference.tdim, order)
         super().__init__(reference, order, poly, dofs, reference.tdim, 1)
 
+    @property
+    def lagrange_subdegree(self) -> int:
+        return self.order
+
+    @property
+    def lagrange_superdegree(self) -> typing.Optional[int]:
+        return self.order
+
+    @property
+    def polynomial_subdegree(self) -> int:
+        return self.order
+
+    @property
+    def polynomial_superdegree(self) -> typing.Optional[int]:
+        return self.order * 2
+
     names = ["Bogner-Fox-Schmit", "BFS"]
     references = ["quadrilateral"]
     min_order = 3
     max_order = 3
     continuity = "C0"
     # continuity = "C1"
+    value_type = "scalar"
     last_updated = "2023.05"