Mortar methods are discretization methods for partial differential equation

Partial differential equation

In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

s, which use separate finite element discretization on nonoverlapping subdomains. The meshes on the subdomains do not match on the interface, and the equality of the solution is enforced by Lagrange multipliers

Lagrange multipliers

In mathematical optimization, the method of Lagrange multipliers provides a strategy for finding the maxima and minima of a function subject to constraints.For instance , consider the optimization problem...

, judiciously chosen to preserve the accuracy of the solution. Mortar discretizations lend themselves naturally to the solution by iterative domain decomposition methods such as FETI

FETI

In mathematics, in particular numerical analysis, the FETI method is an iterative substructuring method for solving systems of linear equations from the finite element method for the solution of elliptic partial differential equations, in particular in computational mechanics In each iteration,...

 and balancing domain decomposition

Balancing domain decomposition

In numerical analysis, the balancing domain decomposition method is an iterative method to find the solution of a symmetric positive definite system of linear algebraic equations arising from the finite element method . In each iteration, it combines the solution of local problems on...

 In the engineering practice in the finite element method, continuity of solutions between non-matching subdomains is implemented by multiple-point constraints.