High-Order Invariant-Domain Preserving Continuous Finite Elements via Graph-Poisson Convex Limiting (opens in new tab)

We develop a high-order invariant-domain preserving continuous finite element method for nonlinear scalar conservation laws. The method combines a residual-viscosity high-order discretization with a low-order invariant-domain scheme constructed on a fine $\mathbb P_1$ submesh induced by the high-order nodal points. This separation avoids the restrictions caused by nonpositive lumped masses and overly wide high-order graph stencils. The high- and...