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We analyze a discontinuous Galerkin FEM-BEM scheme for a second order elliptic transmission problem posed in the three-dimensional space. The symmetric variational formulation is discretized by nonconforming Raviart-Thomas finite elements on a general partition of the interior domain coupled with discontinuous boundary elements on an independent quasi-uniform mesh of the transmission interface. We prove (almost) quasi-optimal convergence of the method and confirm the theory by a numerical experiment. In addition, we consider the case when continuous rather than discontinuous boundary elements are used.
We introduce a coupled finite and boundary element formulation for acoustic scattering analysis over thin shell structures. A triangular Loop subdivision surface discretisation is used for both geometry and analysis fields. The Kirchhoff-Love shell e
Discontinuous Galerkin (DG) methods for hyperbolic partial differential equations (PDEs) with explicit time-stepping schemes, such as strong stability-preserving Runge-Kutta (SSP-RK), suffer from time-step restrictions that are significantly worse th
We propose and analyze novel adaptive algorithms for the numerical solution of elliptic partial differential equations with parametric uncertainty. Four different marking strategies are employed for refinement of stochastic Galerkin finite element ap
A local discontinuous Galerkin (LDG) method for approximating large deformations of prestrained plates is introduced and tested on several insightful numerical examples in our previous computational work. This paper presents a numerical analysis of t
We consider the convergence of adaptive BEM for weakly-singular and hypersingular integral equations associated with the Laplacian and the Helmholtz operator in 2D and 3D. The local mesh-refinement is driven by some two-level error estimator. We show