Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 309, Issue -, Pages 364-387Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2016.06.001
Keywords
Cut elements; Wave equation; Immersed boundary
Funding
- Swedish Research Council [2014-6088]
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We give a weak formulation for solving the wave equation (u=del(2)u+f) on a 2-dimensional immersed domain. In the spatial finite element discretization, boundaries do not conform to element boundaries. Dirichlet and Neumann boundary conditions are enforced weakly by Nitsche's method. Additional penalty terms act on the gradient jumps over the interior faces of the elements cut by the boundary. These terms ensure a non-stiff temporal system, which makes it possible to perform explicit time stepping. We give optimal a priori error estimates: second order accuracy for u-u(h) and u-u(h), and first order accuracy for del(u-u(h)) in L2-norm. Numerical results verify this. (C) 2016 Elsevier B.V. All rights reserved.
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