Can you perform Richardson extrapolation to estimate exact solution from my mesh study?
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I have performed Richardson extrapolation to estimate the exact solution for some nonlinear equations. The mesh used to generate the solutions is fairly coarse, 18 cells, but I find the error in the extrapolation is small, at 0.0021. I will discuss some aspects of my method, and ask if you can perform Richardson extrapolation in a similar way. Section: 3% Error I will discuss three aspects of my method that seem helpful in estimating the exact solution. The first is that Richardson extrapolation
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In recent years, Richardson extrapolation has been used by many numerical analysts to extract exact solutions from their finite element results. I conducted a mesh study to demonstrate the feasibility of this method and report the results in my paper. In my analysis, I used mesh size increment of 1/2 as the fundamental element size to test the extrapolation on the following mesh. I started with 20 elements, and the solution on this mesh was given by an extrapolation factor of 2.007. On my
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The results of my mesh study indicate a maximum efficiency of 131% for solving a linear differential equation with a continuous first-order ordinary differential equation. For a discrete first-order ODE, I achieved 160% efficiency, or 91% accuracy. dig this My results are consistent with the original numerical study by Wen (2013). Wen’s numerical solutions were obtained through Richardson extrapolation. He solved the differential equation iteratively using the numerical methods. In fact, Richardson extrapolation has been used to obtain exact solutions for many
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“Most of this study is about the solution, which means that in most cases the mesh is enough for your needs. You should not need more than 5 elements to determine your solution in such cases. When it is needed, the solution gets more precise, and we call it exact solution. This study should demonstrate the potential for efficient and powerful algorithms for extrapolation of solutions from mesh.” Title: Can you perform Richardson extrapolation to estimate exact solution from my mesh study? Section: Mesh Extrapolation I did not include the word Mesh
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“Richardson extrapolation is a process that allows you to calculate an accurate solution of a partial differential equation in a non-uniform grid. With this technique, the exact solution is found using only the first few points in the mesh. This technique is commonly used in fluid dynamics, as it is able to capture the local interactions between the fluid and its environment. In this context, it is commonly used to calculate the pressure distribution in a fluid layer. In my current project, I am performing a mesh study using Python’s built-in finite difference methods. I have
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I wrote my dissertation project at UC Berkeley in Spring 2022, exploring various finite element (FE) extensions for the inverse problem for 3D fluid/structure interaction (FSI) problems, and one of the extensions I investigated was Richardson extrapolation. his response Here’s what I found. Richardson extrapolation is a standard approach in many finite element methods to improve the convergence and accuracy of finite differences for solutions with discontinuous interface behavior. In particular, Richardson extrapolation makes the solution of a problem on