# Questions tagged [pde]

Partial differential equations (PDEs) are equations that relate the partial derivatives of a function of more than one variable. This tag is intended for questions on modeling phenomena with PDEs, solving PDEs, and other related aspects.

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106 views

### FEM : energy minimization VS PDE solving

Engineering FEM When I studied engineering, I learned the traditional approach for finite elements for elasticity. The point was to solve the PDE $-div(\sigma)=f$ as: Multiply your PDE with a test ...
109 views

### Wave equation, wave is bouncing off Neuman boundary

Wave equation. Mixed BC. Applied Neuman boundary condition ($\frac{\partial u}{\partial x}\big|_N=0$) to the RHS of the domain You may observe the sharp edge in the middle of the string in the image ...
63 views

### Finite element modelling of thermal expansion of 3D solid bodies

I want to solve the thermal expansion of solid by using FEM approach. When I developed the model based on the the principle the minimum potential energy, the solutions for thermal expansion are not ...
537 views

### How to simulate thermal expansion in a 2D plane using FEA?

I am trying to model 2D thermal expansion of a square area inside another square using FEATool. I have simulated plane strain by incorporating forces pointing along the $[1 \,\,\, -1]^T$ direction ...
141 views

### Non-reflective boundary condition

I'm currently solving incompressible Navier-Stokes system of equations with periodic flow and high viscosity. Is there any outlet boundary types that avoids the reflection of flow from the outlet back ...
297 views

### Semi-infinite domain transformation

Question is mostly related to literature or suggestions. Given a semi infinite domain: $x=[0; +\infty);y=[0; +\infty)$. Willing to transform it to computational domain of: $[0,1]\times[0,1]$. I did ...
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### introduction to non-overlapping domain decomposition in 1D

I am new to domain decomposition and have been searching in google for an introduction in 1D which goes over the complete procedure from the continuous to the discrete problem as well as the algorithm ...
181 views

### Continuation of solution to $-\nabla\cdot (k(x,y)\nabla u)=f$

I'm trying to solve the following problem, I had previously opened another discussion for the implementation and well, it seems that it has turned out well, it can be found here. I need to calculate ...
356 views

### Implementing routine for $-\nabla\cdot (k(x,y) \nabla u)=f$ in Matlab

I am solving the Poisson Equation for 2D given by the following expression: $$-\nabla\cdot (k(x,y) \nabla u)=f$$ in a rectangle with Dirichlet conditions on the boundary using Matlab. In principle I ...
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### Elliptic PDE finite volume method with Dirichlet boundary condition

I want to discretize the following equation using a Finite Volume Method $$\nabla \cdot (a(x)\nabla u)=f(x)\\x\in \Omega \subset \mathbb{R}^2 \\u_{|\partial\Omega}=g$$ I'm using Voronoi cells here: ...
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### Stability plot of upward difference implicit time

I am analyzing the stability of 1D convection (advection) equation as shown in the picture. When I derive the equations as shown I want to get rid of the complex number. I`m asking if those stability ...
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### High Running Time and Suboptimal Accuracy of 2D Wave Equation Solver with Finite Differences

Im trying to solve the following 2D wave equation: $$u_{tt} = u_{xx} + u_{yy}, \hspace{3mm} u(x,y,0) = \cos(4 \pi x) \sin(4 \pi y), \hspace{3mm} u_t(x,y,0) = 0$$ with the periodic boundary condition ...
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### Trouble Implementing 1d Wave Equation Finite Difference Solver

Im trying to solve the 1d Wave Equation on $x \in \mathbb{R}, t > 0$: $$u_{tt} = c^2u_{xx}, \hspace{5mm} u(x,0) = \cos(4 \pi x), \hspace{5mm} u_t(x,0) = 0$$ with $c = 1$ and a periodic boundary ...
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### Solving DAE with higher index

I want to solve 7 coupled differential equations in MATLAB. I used the method of lines (MOL) to convert them to a system of DAEs. I then attempted to solve this system using ode15s. Unfortunately an ...
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### Divergence on wave equation simulation

I'm currenly working on my own PDE solver for non-linear simulations in python. I've done succesfully simulations for KdV and Fisher's equation, but now I'm playing with second order derivatives in ...
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### Solving Laplace equation with constraint on boundary

I have found the following PDE problem in a paper: Essentially, we have a rectangular domain where there is a unknown interface $z=\xi(x)$ (liquid-air interface) separating the domain into two medium ...
Find the solution to the Cauchy problem consisting of the wave equation : $$u_{xx}-u_{yy}=0$$ together with initial conditions: $$u(x,0)=0,$$ $$u_{y}(x,0)=g(x)$$ for some known initial datum $g$. Is ...