numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

, mortar methods are

discretization method In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical ...

s for

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s, which use separate

finite element The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat t ...

discretization on nonoverlapping subdomains. The

mesh A mesh is a barrier made of connected strands of metal, fiber, or other flexible or ductile materials. A mesh is similar to a web or a net in that it has many attached or woven strands. Types * A plastic mesh may be extruded, oriented, ex ...

es on the subdomains do not match on the interface, and the equality of the solution is enforced by

Lagrange multipliers In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied e ...

, judiciously chosen to preserve the accuracy of the solution.Y. Maday, C. Mavriplis, and A. T. Patera, ''Nonconforming mortar element methods: application to spectral discretizations'', in Domain decomposition methods (Los Angeles, CA, 1988), SIAM, Philadelphia, PA, 1989, pp. 392--418. B. I. Wohlmuth, ''A mortar finite element method using dual spaces for the Lagrange multiplier'', SIAM J. Numer. Anal., 38 (2000), pp. 989--1012. Mortar discretizations lend themselves naturally to the solution by iterative

domain decomposition method In mathematics, numerical analysis, and numerical partial differential equations, domain decomposition methods solve a boundary value problem by splitting it into smaller boundary value problems on subdomains and iterating to coordinate the solu ...

s such as FETI and

balancing domain decomposition In numerical analysis, the balancing domain decomposition method (BDD) is an iterative method to find the solution of a symmetric positive definite system of linear algebraic equations arising from the finite element method.J. Mandel, ''Balancing d ...

M. Dryja, ''A Neumann-Neumann algorithm for a mortar discretization of elliptic problems with discontinuous coefficients'', Numer. Math., 99 (2005), pp. 645--656. L. Marcinkowski, ''Domain decomposition methods for mortar finite element discretizations of plate problems'', SIAM J. Numer. Anal., 39 (2001), pp. 1097--1114 (electronic). D. Stefanica, ''Parallel FETI algorithms for mortars'', Appl. Numer. Math., 54 (2005), pp. 266--279. G. Pencheva and I. Yotov, ''Balancing domain decomposition for mortar mixed finite element methods'', Numer. Linear Algebra Appl., 10 (2003), pp. 159--180. Dedicated to the 60th birthday of Raytcho Lazarov. In the engineering practice in the finite element method, continuity of solutions between non-matching subdomains is implemented by multiple-point constraints.

References

Domain decomposition methods {{mathapplied-stub