# Questions tagged [adaptive-mesh-refinement]

For questions about AMR, a technique for dynamically updating the precision of a grid to ensure a certain accuracy for a given region.

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### numerical integration of integrals in the p-adaptive version of the finite element method

In the p-adaptive version of the finite element method, elements are allowed to have shape functions with arbitrary different polynomial orders. Therefore regarding a 2D problem with quadrilateral ...
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### Mesh refinement in the Finite Element Method

I need some good references on how to implement programmatically the hp-refinement of meshes in the Finite Element Method in two/three-dimension. I've searched the web a lot and read many articles and ...
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### Comparison on adaptive mesh refinement on finite elements and finite differences

My current work requires using (Adaptive Mesh Refinement) AMR to resolve multi scale physics. I have a general question whether finite element is better than finite difference in this aspect or not. I ...
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### Connectivity of octree as grid

What is the algorithm which transforms the octree/quadtree into a grid? i.e, getting the adjacency or connectivity between the cells in order to be able to perform interpolation, gradient,...etc. I am ...
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### How to deal with transition elements in adaptive fem

It is necessary for me to solve a Poisson equation by adaptive finite element method with transition elements technique to get conforming mesh. For the first local refinement everything is OK, ...
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### Non-uniform finite difference Adaptive Mesh Refinement

Assuming that the crosses in the figure below are unknowns in a vertex-centered finite difference scheme in an Adaptive Mesh, how can I calculate the double derivate (Laplacian) at the Red x ? The Red ...
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### Finite element results by different meshes

There are some technique to generate mesh in a domain. My qustion is that: Is there any difference between the results using different techniques for mesh generation? If yes which one is better. For ...
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### Refinement in AMR

Assume I start with an 8x8 coarse mesh (see Fig 1) where the vertices (except boundary vertices) represent the unknown variable. After iterative approximation - I ...
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### Implementing Finite Difference Adaptive Mesh Refinement code

For a start I need to implement a 2-D, vertex centered, finite difference scheme, Adaptive mesh refinement serial code. I have the following doubts before starting: Is the input to AMR (say 2-D) ...
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### Strategies for controlling number of new elements in adaptive mesh refinement

I am working on adaptive techniques for solving some elliptic equations. The technique is based on residual on elements. My problem is that when I use a predefined tolerance for refining elements, the ...
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### Using finite element error estimators for adaptive mesh refinement

I am in the process of implementing adaptive mesh refinement for a finite element code that solves the Poisson equation. I have had some trouble finding good references on deciding which elements to ...
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### unstructured grid AMR

Are there libraries for conducting parallel AMR on an unstructured grid ? For a finite volume code, polyhedral cells with arbitrarily shaped faces are as easy to handle as hexahedra, and infact ...
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### How to implement adaptive mesh refinement using conformal triangles

I am trying to implement adaptive mesh refinement for a finite element code. The code uses (at least for now) linear triangles and so when I do the mesh refinement I want the triangular mesh to remain ...
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### Finite element mesh software

I'm looking for a program to obtain meshes to finite element codes 2D and 3D as complete as possible, preferably in fortran 90 or C/C++. For example, softwares "Triangle" or "TetGen" generate meshes ...
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### Time advance in Adaptive Mesh Refinement method

I am working on solving complex system of 2D PDEs governing the behaviour of plasma in a gas lamp during discharge. Recent tests have shown that because of steep gradients in temperature field and ...
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### Conservation at grid interface in adaptive mesh refinement

I am using adaptive mesh refinement to solve one dimensional inviscid Burgers equation. However I am facing some difficulty to handle grid interfaces which are not uniform (coarse-fine grid interface)....
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### Adaptive mesh refinement basic conceptual problem

I am a beginner in adaptive mesh refinement (AMR). After I am done with the first two papers by Dr. Marsha Berger, I was trying to write my own code for a problem which has a parabolic partial ...
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### How can I compare errors in PDE solvers with non-uniform grids?

Is there a standard approach to testing codes with refined regions? Specifically, I am interested in testing whether the refinement is working correctly. For the sake of simplicity, let's consider a (...
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### Adaptive mesh refinement algorithms and the difference between AMR and moving mesh

I'm working on my thesis and a part of it has to do with adaptive mesh refinement. As a computer science major, I'm not too familiar with this field. The best way I can put my knowledge of AMR is: I ...
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### Fast methods to solve an elliptic PDE if high accuracy is needed only in part of the domain

Does someone know a method to get cheap approximation of harmonic problems (and possibly local approximations)? Let me explain: I need to compute the solution of an harmonic problem ...
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### Adaptive Mesh vs Uniform Mesh for multiple source/boundary/initial Data

I'm going to ask some beginners' questions. Adaptive mesh can save many DOFs than a uniform mesh. But it also needs to solve linear systems changing with mesh adaptive process. Is this not problem? ...
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### Meshes in codes that do AMR

In light of this question and some stuff I read online I am wondering if large FE libs (e.g., deal.ii, libmesh etc.) that do AMR keep the entire mesh or possibly a coarse version of the entire mesh on ...
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### Finite Element Method vs Extended Finite Element Method (FEM vs XFEM)

What are main differences between FEM and XFEM? When should we (not) use XFEM intead of FEM and vice versa? In other words, when I meet a new problem, how I can know to use which one of them?
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