I want to find a weak form to Navier equations and obtain a solution formulation . I am interested in solving this problem using a finite element solver for which we need to introduce these equations in weak form. Can anyone help me in this regard? What is a higher-order continuity in the FEM approximation. This is challenge with the FEM which is based the Lagrange basis functions. To overcome the shortcomings, should we use the isogemetric analysis being based on the NURBS basis functions? How FEM cover this shortage for solving this type of equations?

Thanks in advance for your guidance.

how I can solve this PDE equation with four boundary conditions mentioned in the attached file?

It seems that this pde needs four boundary conditions. One of them is defined on a curved domain that its function is provided.

Data related to function phi in boundary condition is attached as an excel file.

a similar procedure is provided in this paper

townsend.pdf

Thanks

pde.mw

Book1.xlsx

By considering matrix A and having three conditions mentioned in maple file, Matrix A  has four zero eigenvalues ​​and one non-zero eigenvalue that are reported in maple file by applying three conditions.

The goal is to obtain five Eigenvectors (V__1` ,`V__2` ,`V__3` ,`V__4` ,`V__5`) corresponding to these five eigenvalues ​​such that they have following form.

1-The first Eigenvector should be v1 = [-, -, -, 0,0] that the three dashes can be whatever, but the last two numbers must be 0 and 0.

2- The second Eigenvector should be v2 = [-, -, -, 0,0] where the three dashes can be anything but the last two numbers must be 0 and 0.

3- The third Eigenvector must be v3 = [-, -, -, 1,0], which three dashes are whatever , but the last two numbers must be 1 and 0.

4-The fourth Eigenvector should be v4 = [-, -, -, 0,1] that those three dashes can be whatever, but the last two numbers must be 0 and 1.
 
5-The fifth  Eigenvector should be v5 = [-, -, -, 0,0] that those three dashes can be whatever, but the last two numbers must be 0 and 0.

for more details please see maple file.

How I can find this Eigenvectors by considering mentioned points.

Thanks

EIGENVECTOR.mw

How I can solve following differential equations.?

I want to plot phase diagrams versus time.

diff(xi[i](t), t) versts t (i=1,2,3,4,5,6)

66.mw

Hello,

How I can Plot this structure using define new coordinate such as cylinderical om\ne or addcoords?

plot.mw