Weak Enforcement of Boundary Conditions for Maxwell’s Problem Using the Linked Lagrange Multiplier Method

Date

2025-01-01

Author

Codina, Ramon
Türk, Önder

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In this study, we propose a finite element approximation of Maxwell’s problem with the prescription of essential boundary conditions in a weak way that is based on a linked Lagrange multiplier approach. We consider an augmented formulation with the gradient of a scalar field that allows the imposition of the divergence free condition of the magnetic field. In order to prescribe the Dirichlet type boundary conditions, we present the so called linked Lagrange multiplier method. In this methodology, the boundary conditions are imposed by means of Lagrange multipliers that are related to the main unknowns through least squares terms. In this way, the Lagrange multipliers can be condensed feasibly instead of considering them to be independent variables. We provide a numerical test to show that the proposed approach is capable of successfully approximating the solution of a benchmark problem having both smooth and singular solutions. The results obtained from the proposed scheme are compared with those obtained by using Nitsche’s method for imposing the boundary conditions, showing excellent agreements.

Subject Keywords

Linked Lagrange Multiplier Method, Maxwell’s Problem, Weak Boundary Conditions

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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105004254639&origin=inward
https://hdl.handle.net/11511/114848

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Graduate School of Applied Mathematics, Conference / Seminar