Choice of the family of the Basis Functions
As I have learned for now, there are several families of Polynomial-type Basis functions (Lagrange, Serendipity, Hermite, ...).
My question is beside the order of the elements which affects the order of the Polynomial of the basis functions (Linear, Quadratic, Cubic).
How it comes that in some problems we use Lagrange family and others we use other families?
Does the choice of the Polynomial family depend on the problem we are facing (Linear/Nonlinear, extension/pressure, bending/torsion)?
Supposing that we have chosen a certain geometry of elements (Tetra or Hexa) how can the choice of the family of the basis functions affect the accuracy of the results for the same types of element and same mesh?
Does anyone know about something about this issue?
interpolation finite-element-method lagrange-interpolation
asked Dec 13 '18 at 10:36
Walid AmehriWalid Amehri
61
add a comment |
As I have learned for now, there are several families of Polynomial-type Basis functions (Lagrange, Serendipity, Hermite, ...).
My question is beside the order of the elements which affects the order of the Polynomial of the basis functions (Linear, Quadratic, Cubic).
How it comes that in some problems we use Lagrange family and others we use other families?
Does the choice of the Polynomial family depend on the problem we are facing (Linear/Nonlinear, extension/pressure, bending/torsion)?
Supposing that we have chosen a certain geometry of elements (Tetra or Hexa) how can the choice of the family of the basis functions affect the accuracy of the results for the same types of element and same mesh?
Does anyone know about something about this issue?
interpolation finite-element-method lagrange-interpolation
asked Dec 13 '18 at 10:36
Walid AmehriWalid Amehri
61
See : List of FEM related publications . Maybe there is something you can use in there.
– Han de Bruijn
Dec 15 '18 at 16:12
add a comment |
As I have learned for now, there are several families of Polynomial-type Basis functions (Lagrange, Serendipity, Hermite, ...).
My question is beside the order of the elements which affects the order of the Polynomial of the basis functions (Linear, Quadratic, Cubic).
How it comes that in some problems we use Lagrange family and others we use other families?
Does the choice of the Polynomial family depend on the problem we are facing (Linear/Nonlinear, extension/pressure, bending/torsion)?
Supposing that we have chosen a certain geometry of elements (Tetra or Hexa) how can the choice of the family of the basis functions affect the accuracy of the results for the same types of element and same mesh?
Does anyone know about something about this issue?
interpolation finite-element-method lagrange-interpolation
asked Dec 13 '18 at 10:36
Walid AmehriWalid Amehri
61
As I have learned for now, there are several families of Polynomial-type Basis functions (Lagrange, Serendipity, Hermite, ...).
My question is beside the order of the elements which affects the order of the Polynomial of the basis functions (Linear, Quadratic, Cubic).
How it comes that in some problems we use Lagrange family and others we use other families?
Does the choice of the Polynomial family depend on the problem we are facing (Linear/Nonlinear, extension/pressure, bending/torsion)?
Supposing that we have chosen a certain geometry of elements (Tetra or Hexa) how can the choice of the family of the basis functions affect the accuracy of the results for the same types of element and same mesh?
Does anyone know about something about this issue?
interpolation finite-element-method lagrange-interpolation
interpolation finite-element-method lagrange-interpolation
asked Dec 13 '18 at 10:36
Walid AmehriWalid Amehri
61
asked Dec 13 '18 at 10:36
Walid AmehriWalid Amehri
61
asked Dec 13 '18 at 10:36
Walid AmehriWalid Amehri
61
asked Dec 13 '18 at 10:36
Walid AmehriWalid Amehri
61
asked Dec 13 '18 at 10:36
Walid AmehriWalid Amehri
61
61
See : List of FEM related publications . Maybe there is something you can use in there.
– Han de Bruijn
Dec 15 '18 at 16:12
add a comment |
See : List of FEM related publications . Maybe there is something you can use in there.
– Han de Bruijn
Dec 15 '18 at 16:12
See : List of FEM related publications . Maybe there is something you can use in there.
– Han de Bruijn
Dec 15 '18 at 16:12
See : List of FEM related publications . Maybe there is something you can use in there.
– Han de Bruijn
Dec 15 '18 at 16:12
add a comment |
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See : List of FEM related publications . Maybe there is something you can use in there.
– Han de Bruijn
Dec 15 '18 at 16:12