- document
-
Jain, V. (author), Palha, A. (author), Gerritsma, M.I. (author)In this work we use algebraic dual spaces with a domain decomposition method to solve the Darcy equations. We define the broken Sobolev spaces and their finite dimensional counterparts. A global trace space is defined that connects the solution between the broken spaces. Use of algebraic dual spaces results in a sparse, metric-free...journal article 2023
- document
-
Zhang, Y. (author), Palha, A. (author), Gerritsma, M.I. (author), Rebholz, Leo G. (author)We introduce a mimetic dual-field discretization which conserves mass, kinetic energy and helicity for three-dimensional incompressible Navier-Stokes equations. The discretization makes use of a conservative dual-field mixed weak formulation where two evolution equations of velocity are employed and dual representations of the solution are...journal article 2022
- document
-
Jain, V. (author), Zhang, Y. (author), Palha, A. (author), Gerritsma, M.I. (author)Given a sequence of finite element spaces which form a de Rham sequence, we will construct dual representations of these spaces with associated differential operators which connect these spaces such that they also form a de Rham sequence. The dual representations also need to satisfy the de Rham sequence on the domain boundary. The matrix...journal article 2020