Analysis of a Weak Galerkin Mixed Formulation for Modified Maxwell’s Equations
In this paper, we are interested in studying a mixed formulation of weak Galerkin type to approach the electric field and a Lagrange multiplier, which are solutions of a problem deriving from Maxwell’s equations. Our numerical scheme is formed with stable finite elements constructed of usual polynom...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/24/3901 |
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| Summary: | In this paper, we are interested in studying a mixed formulation of weak Galerkin type to approach the electric field and a Lagrange multiplier, which are solutions of a problem deriving from Maxwell’s equations. Our numerical scheme is formed with stable finite elements constructed of usual polynomials of degree <i>k</i> for the electric field and of degree <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> for the Lagrange multiplier; its consistency and well-posedness are shown. Some optimal error estimates are proven and tested numerically in a bounded subdomain of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mn>2</mn></msup></semantics></math></inline-formula>. |
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| ISSN: | 2227-7390 |