Boundary value problem: local stifness matrix

sara_87
Messages
748
Reaction score
0

Homework Statement



Given a BVP:

\Delta(u)+u=1 in \Omega
u=0 on \partial\Omega
using linear piecewise functions,
calculate the corresponding local stiffness matrix on the reference triangle :
{(x,y); 0<=x<=1, 0<=y<=1-x}.

The domain is a square with one point in the middle (at (0.5,0.5))

Homework Equations





The Attempt at a Solution



Does anyone know where i can start?
 
Physics news on Phys.org
which numerical method are you using?
 
I am using the finite element method.
I forgot to mention, i fixed my problem, i know how to do this question :)
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Green's Function with Neumann Boundary Conditions
Replies
8
Views
3K
Another max value on surface (no boundaries)
Replies
8
Views
2K
Is this vector in the image of the matrix?
Replies
4
Views
2K
Boundary condition for PDE heat eqaution
Replies
1
Views
2K
Green's function for a boundary value problem
Replies
2
Views
2K
Is d'Alembert's Formula Correct for Neumann Boundary Conditions in PDEs?
Replies
4
Views
2K
Green's Function Boundary Conditions
Replies
8
Views
2K
Finite Element MATLAB Code for Solving Boundary Value Problems
Replies
1
Views
2K
Solving Laplace Equations using this boundary conditions?
Replies
1
Views
2K
How should I show that ## B ## is given by the solution of this?
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top