Meshes

Mesh Specification

Finite element meshes are specified in the (node,elem) structure due to Long Chen. For the standard elements used in this package, we describe a geometric figure by a triangulation. The nodes are the vertices of the triangle and the elements are the triangles themselves. These are encoded as follows:

Row $i$ of node is an $(x,y)$ (or $(x,y,z)$) pair which specifies the coordinates of the $i$th node.
Row $j$ of elem are the indices of the nodes which make the triangle. Thus in 2D each row has three numbers.

For example, to know the $(x,y)$ locations of the vertices of triangle $j$, we would see that node[elem[j,i],:] are the $(x,y)$ locations of the $i$th vertex for $i=1,2,3$.

For more information, please see Programming of Finite Element Methods by Long Chen.

Mesh Type

FiniteElementDiffEq.FEMmesh
FiniteElementDiffEq.SimpleMesh
DiffEqBase.Mesh

Mesh Generation Functions

FiniteElementDiffEq.findboundary
FiniteElementDiffEq.setboundary
FiniteElementDiffEq.fem_squaremesh
FiniteElementDiffEq.notime_squaremesh
FiniteElementDiffEq.parabolic_squaremesh
Base.size(::StokesDiffEq.FDMMesh)

Example Meshes

DiffEqProblemLibrary.meshExample_bunny — Function.

meshExample_bunny() : Returns a 3D SimpleMesh.

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DiffEqProblemLibrary.meshExample_flowpastcylindermesh — Function.

meshExample_flowpastcylindermesh() : Returns a 2D SimpleMesh.

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DiffEqProblemLibrary.meshExample_lakemesh — Function.

meshExample_lakemesh() : Returns a 2D SimpleMesh.

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DiffEqProblemLibrary.meshExample_Lshapemesh — Function.

meshExample_Lshapemesh() : Returns a 2D SimpleMesh.

source

DiffEqProblemLibrary.meshExample_Lshapeunstructure — Function.

meshExample_Lshapeunstructure() : Returns a 2D SimpleMesh.

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DiffEqProblemLibrary.meshExample_oilpump — Function.

meshExample_oilpump() : Returns a 3D SimpleMesh.

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DiffEqProblemLibrary.meshExample_wavymesh — Function.

meshExample_wavymesh() : Returns a 2D SimpleMesh.

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DiffEqProblemLibrary.meshExample_wavyperturbmesh — Function.

meshExample_wavyperturbmesh() : Returns a 3D SimpleMesh.

source

Plot Functions

The plot functionality is provided by a Plots.jl recipe. What is plotted is a "trisurf" of the mesh. To plot a mesh, simply use:

plot(mesh::Mesh)

All of the functionality (keyword arguments) provided by Plots.jl are able to be used in this command. Please see the Plots.jl documentation for more information.