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

, mortar methods are discretization methods 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 function. The function is often thought of as an "unknown" to be solved for, similarly to ...

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 models, mathematical modeling. Typical problem areas of interest include the traditional fields of struct ...

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, e ...

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 ...

, 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 methods such as FETI and balancing domain decompositionM. 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