Finite Element Method

The finite element method is a numerical method to solve differential equations over arbitrary-shaped domains. The finite element method is implemented in NDSolve as a spacial discretization method, and the primary usage of the finite element method is through NDSolve. Furthermore, interfaces to low-level finite element functionality are provided.

NDSolve numerically solve differential equations

NIntegrate numerically integrate

NDEigensystem numerically compute differential eigenvalues and eigenvectors

Mesh Generation

ToBoundaryMesh convert various input to a boundary mesh

ToElementMesh convert various input to a full mesh

ToGradedMesh convert Line graphics primitives input to a graded mesh

ElementMeshRegionProduct the Cartesian products of element meshes

ElementMesh a mesh data structure

NumericalRegion a symbolic and mesh data structure

PointElement  ▪  LineElement  ▪  TriangleElement  ▪  QuadElement  ▪  TetrahedronElement  ▪  PrismElement  ▪  HexahedronElement


InitializePDECoefficients initialize partial differential equation coefficients

InitializeBoundaryConditions initialize boundary conditions

InitializePDEMethodData initialize partial differential equation method data

PDECoefficientData  ▪  BoundaryConditionData  ▪  FEMMethodData


DiscretizePDE discretize initialized partial differential equations

DiscretizeBoundaryConditions discretize initialized boundary conditions

DiscretizedPDEData  ▪  DiscretizedBoundaryConditionData  ▪  DirichletCondition  ▪  NeumannValue  ▪  PeriodicBoundaryCondition


DeployBoundaryConditions deploy discretized boundary conditions into discretized partial differential equations

LinearSolve solve linear systems of equations

PDESolve solve linear and nonlinear systems of equations

Post Processing

ProcessPDESolutions process solution data into InterpolatingFunction objects.

ElementMeshInterpolation creates an InterpolatingFunction from a solution over a mesh