# Questions tagged [numerical-analysis-of-pde]

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### Coonvergence rate for the clamped plate problem when approximating with polygonal domains

I'm trying to understand Ridgeway Scott's "A survey of displacement methods for the plate bending problem" [1]. In chapter four he is talking about polygonal approximation and states that ...
25 views

### Peak search for NLS equation solutions

By solving the initial value problem of the NLS equation, I can get a matrix of numerical solutions. I hope to perform a peak search on the matrix of this numerical solution, that is, there are ...
75 views

### Rate of convergence of mollified distributions in Besov spaces with negative regularity

Given a standard mollifier $\rho_\delta$ and a distribution $u \in B^\alpha_{ p, p}$ with $\alpha<0$, $p \in [1, \infty]$ and $B^\alpha_{p,p}$ is a not-homogeneous Besov space, I'm trying to prove ...
• 293
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### Galerkin scheme in $H^s_0(G)\subset L^2(G)\subset H^{-s}(G)$ ($s>0$)

What basis functions are usually choosen if one attempts to conduct a Galerkin finite element method given an evolution triplet $H^s_0(G)\subset L^2(G)\subset H^{-s}(G)$. Where $G$ is a sufficiently ...
• 163
1 vote
24 views

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### Inconsistency in determinability of the solution of a linear first order PDE

Consider the following differential equation: $$\frac{\partial u(x,t)}{\partial t} = - \frac{\partial u(x,t)}{\partial x} + u(x,t) \label{1}\tag{1}$$ with $u(x,0)=f(x)$. The solution of \eqref{1}, ...
• 350
731 views

### What are dissipative PDEs?

I often come across the term dissipative (partial) differential equation in mathematical articles, especially in the context of hypocoercivity and entropy methods. I now have an intuitive idea of ​​...
• 55
1 vote
37 views

### Studying the evolution of laplacian in NS equation

The Navier-Stokes equation in $\mathbb{R}^3$ subjected to no gravitational forces are provided by: \label{Eq1} \dfrac{\partial }{\partial t} \textbf{u} + \left(\textbf{u}\cdot \nabla \...
• 305
173 views

### Where can I find the paper by Tappert and Hardin on split-step Fourier transform method?

The split-step method is a numerical method that can be used to solve a nonlinear PDE (https://en.wikipedia.org/wiki/Split-step_method). Even Wikipedia does not refer to the original authors (F.D. ...
• 101
1 vote
51 views

### Error estimates for inhomogeneous semidiscrete PDE

I have the following semidiscrete problem on a meshed domain $U_h$. Let $V_h$ be linear finite elements on $U_h$, $V_{h0}\subset V_h$ have zero trace on $\partial \Omega_h$, and $V_{h\partial}$ be ...
• 225
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### Approximating solutions to Monge-Ampere from optimal transport plans

I am interested in finding numerical solutions to a Monge-Ampere type equation for applications in physics. Due to the close connection between Monge-Ampere and optimal transport and the well ...
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555 views

1 vote
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### Typo in error a-priori estimate in a discontinuous Galerkin paper?

I'm looking at this famous paper which is available in the link below: Franco Brezzi, LD Marini, Endre Süli, Discontinuous Galerkin methods for first-order hyperbolic problems, Mathematical Models ...
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• 157
1 vote
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### Weird claims and conclusions in "Introduction to Shape Optimization"

I'm trying to understand the notions of Euler and Hadamard derivatives of shape functionals. All the lecture notes and papers on this topic that I've found seem to build up on the books Shapes and ...
• 157
1 vote
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