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.

参考资料参考资料

NDSolve numerically solve differential equations

NIntegrate numerically integrate

Mesh Generation

ToBoundaryMesh convert various input to a boundary mesh

ToElementMesh convert various input to a full mesh

ElementMesh a mesh data structure

PointElement  ▪  LineElement  ▪  TriangleElement  ▪  QuadElement  ▪  TetrahedronElement  ▪  HexahedronElement

Initialization

InitializePDECoefficients initialize partial differential equation coefficients

InitializeBoundaryConditions initialize boundary conditions

InitializePDEMethodData initialize partial differential equation method data

PDECoefficientData  ▪  BoundaryConditionData  ▪  FEMMethodData

Discretization

DiscretizePDE discretize initialized partial differential equations

DiscretizeBoundaryConditions discretize initialized boundary conditions

Solution

DeployBoundaryConditions deploy discretized boundary conditions into discretized partial differential equations

LinearSolve solve linear systems of equations