Entropy solutions of scalar conservation laws are recovered as weak-star limits of nonlocal approximations with averaged fluxes via Hamilton-Jacobi stability.
Finite Volume Methods
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PVD-ONet combines multi-network DeepONet modules with Prandtl and Van Dyke matching conditions to map initial data to solution operators for families of singularly perturbed boundary-layer problems and to infer scaling exponents from sparse observations.
Enforcing semilinearity via local stencil-scale normalization and training on polynomial profiles produces stable, generalizable neural advection schemes with a new flux limiter that improves shape preservation over OSTVD3.
Presents a coupled prediction-correction variant of Hughes' crowd model and uses numerical simulations to suggest progress toward its well-posedness.
Introduces a scalable Bayesian inference framework for nonlinear conservation laws using Gaussian process priors and sparse approximations, enabling accurate forward simulations with UQ and fast posterior recovery on inverse problems.
A generalized flux-corrected transport limiter for systems of conservation laws enforces invariant domain preservation by expressing the high-order solution as a convex combination of low-order invariant-domain-preserving states, applicable to both explicit and implicit time discretizations.
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Invariant domain preserving limiting of time explicit and time implicit discretizations for systems of conservation laws
A generalized flux-corrected transport limiter for systems of conservation laws enforces invariant domain preservation by expressing the high-order solution as a convex combination of low-order invariant-domain-preserving states, applicable to both explicit and implicit time discretizations.