Questions tagged [well-posedness]

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Analysis of nonlinear finite element methods

I have been doing a lot of reading on the development of finite element methods and their analysis using, e.g., functional analysis. I am clear on the formulation of the weak form of a PDE and ...
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How to show that a problem is ill-posed

I was searching around here for a while but I didn't find any discussion on this topic. We know that a problem is well-posed when There is a solution (existence), There is only one solution (...
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3 votes
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Traction -> stress; stress->displacement gradient

If given a displacement gradient tensor, we can easily obtain the stress tensor (using Hooke's law and the strain-displacement relationship), as well as the traction vector. If given a traction, and ...
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Correctly setting boundary condition for periodic linear elasticity problem

From an old, wise engineering book Peterson's Stress Concentration Factors (http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470048247.html page 324) I've got the following problem: There is 2D ...
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Well-posedness of Elasticity Boundary Conditions

For geotechnical engineering problems, it is common to fix a single component of displacement along a boundary as a Dirichlet boundary condition (roller boundary condition). However, I'm having ...
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Is this system of diffusion equations well-posed?

I’m using a standard Crank-Nicholson algorithm to solve this system of two coupled diffusion equations: $$\dot{u} - \dot{v} = \frac{\partial}{\partial x} \left( \alpha(x) \frac{\partial u}{\partial x}...
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2 votes
0 answers
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How to classify chaotic systems from a stability perspective

I am wondering what chaotic systems are from the perspective of numerical analysis. I am talking about 'deterministic chaos' such as for instance the 'logistic map' exhibits it. That is, the solution ...
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9 votes
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Well-posedness of a linear elasticity problem with periodic boundary conditions

For certain applications, such as steady state heat transfer and flow in porous media, it is possible to simulate a much larger (infinite) domain by imposing periodic boundary conditions on opposite ...
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4 votes
1 answer
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variational formulation of linear elasticity

First I'm not 100% sure I'm on the good stack for asking my question. I would like to get a bilinear form for linear elasticity that separate a rotational part from a pure divergence part, so starting ...
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5 votes
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Is the heat equation with Neumann boundary conditions well-posed?

For example I consider a heat equation that I want to solve numerically : $$u_t=u_{xx},$$ In order to have a uniqueness on a computational bounded domain I have to have boundary condition specified ...
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10 votes
1 answer
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Can a numerical scheme be used to determine the well-posedness of an initial or boundary value problem?

I know that we can use mathematical analysis techniques to prove if an IVP or BVP has a solution, is unique, and depends continuously on the boundary / initial values. For some PDE's, particularly ...
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