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?
2026-03-27 23:38:52.1774654732
Finite Element Method vs Extended Finite Element Method (FEM vs XFEM)
993 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in NUMERICAL-METHODS
- The Runge-Kutta method for a system of equations
- How to solve the exponential equation $e^{a+bx}+e^{c+dx}=1$?
- Is the calculated solution, if it exists, unique?
- Modified conjugate gradient method to minimise quadratic functional restricted to positive solutions
- Minimum of the 2-norm
- Is method of exhaustion the same as numerical integration?
- Prove that Newton's Method is invariant under invertible linear transformations
- Initial Value Problem into Euler and Runge-Kutta scheme
- What are the possible ways to write an equation in $x=\phi(x)$ form for Iteration method?
- Numerical solution for a two dimensional third order nonlinear differential equation
Related Questions in FINITE-ELEMENT-METHOD
- What is the difference between Orthogonal collocation and Weighted Residual Methods
- Lagrange multiplier for the Stokes equations
- Does $(q,\nabla u)\lesssim C|u|_1$ implies $\Vert q\Vert_0\lesssim C$?
- How to approximate numerically the gradient of the function on a triangular mesh
- Proving $||u_h||_1^2=(f,u_h)$ for mixed finite elements
- Function in piecewise linear finite element space which satisfies the divergence-free condition is the zero function
- Implementing boundary conditions for the Biharmonic equation using $C^1$ elements.
- Deriving the zero order jump condition for advection equation with a source?
- Definition of finite elements (Ciarlet)
- finite elements local vs global basisfunction
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
The extended finite element method (XFEM) is mainly targeted towards problems with strong or weak discontinuities. By a strong discontinuity I mean a jump in the values of the solution (consider e.g. a crack in the elastic setting) and by a weak discontinuity I mean a jump in the derivative of the solution (might e.g. be due to a strongly discontinuous material parameter field).
The strong discontinuities are represented by basis functions which are discontinuous over the "crack". In addition to the implicit representation of the discontinuity, the set of basis functions is often augmented with some sort of singular basis functions (obtained by asymptotic methods) which attempt to represent the asymptotic behavior of the solution near crack tip.
The alternative to XFEM is of course to use a standard finite element method on a mesh which conforms with the crack. This requires a higher amount of elements but is much easier to implement. Furthermore, the non-standard basis functions of XFEM require a careful planning of the numerical integration rules while constructing the stiffness matrix.
According to my experience, for two-dimensional problems there exists quite well-performing XFEM codes (for example GetFEM++). The three dimensional implementations suffer from the lack of theory of singularities in three dimensional cracks: It's hard to find any accurate asymptotic functions for three dimensional crack singularities and therefore the asymptotic convergence (which is often used to measure the performance of a certain finite element method) will suffer. This reduces the usefulness of the crack tip enrichment and thus the usefulness of XFEM with respect to the standard mesh->solve->remesh->solve->... iteration in crack propagation analyses.