Improved $L^2$-error estimates for the wave equation discretized using hybrid nonconforming methods on simplicial meshes Article Swipe
We present improved $L^2$-error estimates on the time-integrated primal variable for the wave equation in its first-order formulation. The space discretization relies on a hybrid nonconforming method, such as the hybridizable discontinuous Galerkin, the hybrid high-order or the weak Galerkin methods. We consider both equal-order and mixed-order settings on simplices, and include the lowest-order case with piecewise constant unknowns on the faces and in the cells. Our main result is a superclose, resp., optimal bound on the above error in the equal-, resp., mixed-order case. A key result of independent interest to achieve these estimates are novel approximation estimates for an interpolation operator inspired from the hybridizable discontinuous Galerkin literature.
Related Topics
Concepts
Mathematics
Discretization
Piecewise
Applied mathematics
Interpolation (computer graphics)
Operator (biology)
Mathematical analysis
Variable (mathematics)
Discontinuous Galerkin method
Galerkin method
Wave equation
Constant (computer programming)
Polygon mesh
Simple (philosophy)
Space (punctuation)
Key (lock)
Variable coefficient
Mathematical optimization
Constant coefficients
Error analysis
Upper and lower bounds
Approximation error
Metadata
- Type
- article
- Landing Page
- http://arxiv.org/abs/2511.13130
- https://arxiv.org/pdf/2511.13130
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7106094146
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W7106094146Canonical identifier for this work in OpenAlex
- Title
-
Improved $L^2$-error estimates for the wave equation discretized using hybrid nonconforming methods on simplicial meshesWork title
- Type
-
articleOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
-
2025-11-17Full publication date if available
- Authors
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Cockburn, Bernardo, Ern, Alexandre, Khot, RekhaList of authors in order
- Landing page
-
https://arxiv.org/abs/2511.13130Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2511.13130Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2511.13130Direct OA link when available
- Concepts
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Mathematics, Discretization, Piecewise, Applied mathematics, Interpolation (computer graphics), Operator (biology), Mathematical analysis, Variable (mathematics), Discontinuous Galerkin method, Galerkin method, Wave equation, Constant (computer programming), Polygon mesh, Simple (philosophy), Space (punctuation), Key (lock), Variable coefficient, Mathematical optimization, Constant coefficients, Error analysis, Upper and lower bounds, Approximation errorTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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