A robust elliptic grid generator
Journal of Computational Physics
Numerical simulation of gravity waves
Journal of Computational Physics
Traveling water waves: spectral continuation methods with parallel implementation
Journal of Computational Physics
A finite element method for fully nonlinear water waves
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Discontinuous Galerkin Method for Linear Free-Surface Gravity Waves
Journal of Scientific Computing
Quasi ALE finite element method for nonlinear water waves
Journal of Computational Physics
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Journal of Computational Physics
Space-time discontinuous Galerkin method for advection-diffusion problems on time-dependent domains
Applied Numerical Mathematics
Space-time discontinuous Galerkin finite element method for shallow water flows
Journal of Computational and Applied Mathematics
Space-time discontinuous Galerkin finite element method for two-fluid flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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A space-time discontinuous Galerkin (DG) finite element method for nonlinear water waves in an inviscid and incompressible fluid is presented. The space-time DG method results in a conservative numerical discretization on time dependent deforming meshes which follow the free surface evolution. The algorithm is higher order accurate, both in space and time, and closely related to an arbitrary Lagrangian Eulerian (ALE) approach. A detailed derivation of the numerical algorithm is given including an efficient procedure to solve the nonlinear algebraic equations resulting from the space-time discretization. Numerical examples are shown on a series of model problems to demonstrate the accuracy and capabilities of the method.