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A weak Galerkin finite element method for the Navier–Stokes equations
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A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes
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A dual Petrov–Galerkin finite element method for the convection–diffusion equation
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A least-squares finite element method for a nonlinear Stokes problem in glaciology
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Effective implementation of the weak Galerkin finite element methods for the biharmonic equation
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An eXtended Finite Element Method with Algebraic Constraints (XFEM-AC) for problems with weak discontinuities.
Abstract not provided.
B-spline based finite-element method for the stationary quasi-geostrophic equations of the ocean
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A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow
Here we propose a model order reduction technique integrating the Shifted Boundary Method (SBM) with a POD-Galerkin strategy. This approach allows to deal with complex parametrized domains in an efficient and straightforward way. The impact of the proposed approach is threefold. First, problems involving parametrizations of complex geometrical shapes and/or large domain deformations can be efficiently solved at full-order by means of the SBM. This unfitted boundary method permits to avoid remeshing and the tedious handling of cut cells by introducing an approximate surrogate boundary. Second, the computational effort is reduced by the development of a Reduced Order Model (ROM) technique based on a POD-Galerkin approach. Third, the SBM provides a smooth mapping from the true to the surrogate domain, and for this reason, the stability and performance of the reduced order basis are enhanced. This feature is the net result of the combination of the proposed ROM approach and the SBM. Similarly, the combination of the SBM with a projection-based ROM gives the great advantage of an easy and fast to implement algorithm considering geometrical parametrization with large deformations. The transformation of each geometry to a reference geometry (morphing) is in fact not required. These combined advantages will allow the solution of PDE problems more efficiently. We illustrate the performance of this approach on a number of two-dimensional Stokes flow problems.
Effects of misorientation on single crystal plasticity by finite element methods
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Optimal test functions for boundary accuracy in discontinuous finite element methods
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Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods
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A hybrid reconstructed discontinuous Galerkin and continuous Galerkin finite element method for incompressible flows on unstructured grids
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