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- W4382706670 abstract "Linear wave equations sourced by a Dirac delta distribution $delta(x)$ and its derivative(s) can serve as a model for many different phenomena. We describe a discontinuous Galerkin (DG) method to numerically solve such equations with source terms proportional to $partial^n delta /partial x^n$. Despite the presence of singular source terms, which imply discontinuous or potentially singular solutions, our DG method achieves global spectral accuracy even at the source's location. Our DG method is developed for the wave equation written in fully first-order form. The first-order reduction is carried out using a distributional auxiliary variable that removes some of the source term's singular behavior. While this is helpful numerically, it gives rise to a distributional constraint. We show that a time-independent spurious solution can develop if the initial constraint violation is proportional to $delta(x)$. Numerical experiments verify this behavior and our scheme's convergence properties by comparing against exact solutions." @default.
- W4382706670 created "2023-07-01" @default.
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- W4382706670 date "2022-11-29" @default.
- W4382706670 modified "2023-09-26" @default.
- W4382706670 title "Discontinuous Galerkin Method for Linear Wave Equations Involving Derivatives of the Dirac Delta Distribution" @default.
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- W4382706670 doi "https://doi.org/10.1007/978-3-031-20432-6_19" @default.
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