Dimitrios Mitsotakis, Costas Synolakis, Mark Mcguinness
Published 2015-05-28Version 1
A new modified Galerkin / Finite Element Method is proposed for the numerical solution of the fully nonlinear shallow water wave equations. The new numerical method allows the use of low-order Lagrange finite element spaces, despite the fact that the system contains third order spatial partial derivatives for the depth averaged velocity of the fluid. After studying the efficacy and the conservation properties of the new numerical method, we proceed with the validation of the new numerical model and boundary conditions by comparing the numerical solutions with laboratory experiments and with available theoretical asymptotic results.
A priori estimates of a finite element method for fractional diffusion problems by energy arguments
A finite element method for the Monge--Ampère equation with transport boundary conditions
On the Richardson Extrapolation in Time of Finite Element Method with Discrete TBCs for the Cauchy Problem for the 1D Schrödinger Equation
![QR code for arXiv:1505.07795 [math.NA]](http://oss.arxitics.com/images/favicon.svg)