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### Mesh aspect ratio issue with adaptive mesh refinement (AMR)

I am working on implementation of AMR for my finite volume code. Let me use a 2-D mesh to describe my question. Starting with SINGLE initial cell (let the mesh refine level k = 0) as a root of a quad-...
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### Recovery of smoothed continuous stresses using the Z^2 error estimator

I have trouble implementing the $Z^2$ error estimator (The superconvergent patch recovery and a posteriori error estimates. Part 1: the recovery technique by Zienkiewicz and Zhu). For this, I am ...
106 views

### Good references for dual-weighted residual (DWR) method for goal-oriented adaptive mesh refinement (AMR)

Can anyone help me with good references (books or papers) where I can learn about dual-weighted residual (DWR) method for goal-oriented adaptive mesh refinement (AMR)?
180 views

### Finite Difference libray C++

What is the best FD library (or collection of libraries) for C++ codes? I am looking for some data structure implementation that offers the possibility to do parallel computations on adaptively ...
123 views

### Implementation of Z^2 error estimator in Abaqus for adaptive mesh refinement

Currently, I am working on a remeshing routine for my simulations (Abaqus 6.14-1) using python scripts. The simulation deals with the Brinell indentation test and as the remeshing software I use Gmsh ...
680 views

### simple example of an adaptive mesh refinement code

I have been writing an adaptive mesh refinement (amr) code. As a prototype for the code, I have been looking at an adaptive mesh refinement code written by my adviser (written in c). I find looking at ...
304 views

I am graduate student and recently tried to implement quad-tree based AMR. Well I have implemented simple Poisson Solver on node-based quadtree, but I am not sure that my data structure is right. To ...
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191 views

### Flux at coarse-fine mesh grid interface?

I am trying to solve one dimensional inviscid Burger's equation using adaptive mesh refinement. This is the PDE: $$\frac{\delta U}{\delta t} + \frac{\delta F}{\delta x} = 0$$ where the flux F of the ...
212 views

### 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 ...
363 views

### 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, ...
320 views

### 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 ...
140 views

### 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 ...
911 views

### 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) ...
94 views

### 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 ...
189 views

### 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 ...
392 views

### 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 ...
119 views

I want to solve the following differential equation using control volume approach on a Cartesian mesh: $$\frac{\partial T}{\partial t} + \frac{\partial T}{\partial x} + \frac{\partial T}{\partial y}= \... 0answers 348 views ### Adaptive Finite Element Method - Laplace I'm currently attempting to turn my code for solving the laplace equation using finite element approximations into an adaptive one using the dual weighted residual as my error estimator: i.e. my ... 2answers 1k views ### How to discretize Burger's equation? I am trying to solve the very simple one dimensional burgers equation which is:$$\frac{\delta U}{\delta t} + \frac{\delta F}{\delta x} = 0$$where the flux F of some variable U is defined as$$ F= \...
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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 ...
118 views

### 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)....
263 views

### 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 ...
86 views

### 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 (...
238 views

### 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 ...
101 views

### 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 ...
98 views

### 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? ...
346 views

### 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 ...
3k views

### 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?