Theory, implementation, and practice november 9, 2010 springer. The book should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when. The mortar finite element method guide books acm digital library. Ample discussion of the computer implementation of the finite element. The meshes on the subdomains do not match on the interface, and the equality of the solution is enforced by lagrange multipliers, judiciously chosen to preserve the accuracy of the solution.
This thesis is also focused on domain decomposition methods for mortar nite elements. Download introduction to finite element method by j. We employ the concept of the reference element which seems in the authors opinion more suitable for the implementation. Introduction to finite element analysis fea or finite. The general concepts of the schwarz theory were first introduced by dryja and.
However, the implementation of these methods is rather complicated problem which can di. The implementation is thus very natural and embarrassingly parallel, the. The most popular method of this class is the finite element metho d fem. The finite element method fem, or finite element analysis fea, is a computational technique used to obtain approximate solutions of boundary value problems in engineering. The field is the domain of interest and most often represents a physical structure.
Lectures on the finite element method tata institute of. Domain decomposition methods for mortar finite elements. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including. The authors give an introduction to the finite element method as a general computational method for solving partial differential equations pdes approximately. Our main goalhas been to obtain numerical and theoretical performance estimates for these methods of the same form as in the conforming nite element case. Reddy since the practice of the finite element method ultimately depends on ones ability to implement the technique on a digital computer, examples and exercises are designed to let the reader actually compute the solutions of various problems using computers. In this chapter we deal with the implementation of the. The mortar nite element method is a nonconforming domain decomposition technique tailored to handle. Implementation issues are considered in section 6 while the results of numerical experiments illustrating the theory are given in section 7. Basics and some applications of the mortar element method christine bernardi 1, yvon maday 1, and francesca rapetti 2 1 laboratoire jacqueslouis lions, c. Progress toward a new implementation of the mortar finite element. Kut akov a 2 1 department of mathematics, university of west bohemia, pilsen 2 mecas esi s. Pdf the present paper deals with a variant of a non conforming domain decomposition technique. Moreover, we include a description of the necessary data structures.
A mortar finite element method using dual spaces for the. Basics and some applications of the mortar element method. Boundary value problems are also called field problems. The numerical results are showing both the principle and the possibility of practical use of the method. In chapter 5, we analyze the finite element tearing and interconnecting. The central feature of the method is to partition the domain in a systematic manner into an assembly of discrete. The approach taken is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational. In numerical analysis, mortar methods are discretization methods for partial differential equations, which use separate finite element discretization on nonoverlapping subdomains. A domain of interest is represented as an assembly of. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software matlab is and its pdetoolbox. In this section, we present some basic results on sobolev spaces, which are used. The mortar finite element method allows the coupling of different.
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