# Questions tagged [finite-element-method]

A method of obtaining (numerically) approximate solutions to (usually) differential equations. It consists of a method of discretization splitting the domain into disjoint subdomains over each of which the problem has a simpler (approximate) solution, and a method of reassembling those pieces to obtain a solution over the whole domain. It is closely tied to the calculus of variations.

618 questions
Filter by
Sorted by
Tagged with
1 vote
15 views

### purpose of interpolants in Galerkin methods

I am learning about the finite element method in an abstract Banach and Hilbert space setting, especially for an application to differential forms, and I am a bit lost on the big picture about the ...
20 views

### inhomogeneous Helmholtz equation does not obey superposition using FEM

I am trying to solve the in-homogeneous Helmholtz equation with damping and forcing using finite element method (FEM). The equation is; $c^2\nabla^2p - c^2\omega i d \nabla^2p + \omega^2 p = f$ where ...
1 vote
24 views

### Is the weak form on this book about a level set FSI problem wrong?

I'm trying to repeat a level set FSI problem on the book :Level Set Methods for Fluid-Structure Interaction, on the page 89, the provided freefem code define a weak form of the discretized equation ...
12 views

### Solving the weak form

$$K \cdot w^e(x) \cdot \frac{d}{dx}T(x) \Bigg|_{x=0}^{x=L} - \int_0^L K \cdot w^e(x) \cdot \frac{d}{dx}T(x) \, dx + \int_0^L w^e(x) \cdot Q \, dx = 0$$ I am learning Finite element analysis. In this ...
89 views

### why $u \in H^2$ imply zero value of jump $[u] = u^{-}-u^{+}$

in page 13 of simple DG tutorial, it gives following conclusion: Define average $w=\frac{1}{2}\left(w^{-}+w^{+}\right)$ and recall jump $[w]=w^{-}*w^{+}$ then $$[a b]=[a]\{b\}+\{a\}[b]$$ confusing ...
1 vote
29 views

### Discretize Burger's equation with upwind strategy

Let the 1D burgers equation be defined by $\frac{\partial u}{\partial t} + a \frac{\partial u}{\partial x} = v \frac{\partial^2 u}{\partial x^2}$ where $v = \frac{1}{Re}$ where $Re$ is the number of ...
89 views

### How to get shape functions for three node 2d triangular element

I am struggling with the shape function of finite element method. For sake of computation, most often we work with local coordinate. For 1d things are bit clear to me. but for 2d things getting hard ...
1 vote
36 views

29 views

1 vote
47 views

1 vote
42 views

### Rewrite function in a different coordinate system

Let's consider the triangle $\Delta$ in $\mathbb{R}^2$ with the vertices $e_1=(0,0), e_2=(1,0)$ and $e_3=(0,1)$. Let $\mathbb{P}$ denote the set of bivariate polynomials of degree $\leq 1$. In the ...
33 views

### Coordinate transformation of functions

I am given the triangle $\Delta$ in $\mathbb{R}^2$ in which the vertices are given as the points $e_1=(0,0), e_2=(1,0)$ and $e_3=(0,1)$. The space $\mathbb{P}$ is defined as the set of bivariate ...
45 views

### use finite element method to solve the PDE

Hi so I want to use the finite element method to solve this question ∂/∂x (y^2 ∂u/∂x (x,y))+∂/∂y (y^2 ∂u/∂y (x,y))-yu(x,y)=-x (x,y)∈D where the boundary conditions are: u(0,y)=0 for 0.5 ≤y ≤1 ...
1 vote
20 views

### How the solution $u$ converges to the best approximation of the solution $u^{(k)}$ in the $H^1(\Omega)$-norm?

Let $\Omega$ be a polygonal domain in $\mathrm{R}^2$ and let $\mathcal{T}_0, \mathcal{T}_1,...$ be a sequence of triangulations of $\Omega$ formed by standard refinement. Let $\mathcal{P}_k^1$ be the ...
1 vote