The p- and h-p version of the finite element method, an overview
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
The immersed interface method using a finite element formulation
Applied Numerical Mathematics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
The immersed finite volume element methods for the elliptic interface problems
Mathematics and Computers in Simulation - Special issue from IMACS sponsored conference: “Modelling '98”
A rectangular immersed finite element space for interface problems
Scientific computing and applications
Discontinuous Galerkin Methods: Theory, Computation and Applications
Discontinuous Galerkin Methods: Theory, Computation and Applications
Immersed finite element methods for 4th order differential equations
Journal of Computational and Applied Mathematics
Linear and bilinear immersed finite elements for planar elasticity interface problems
Journal of Computational and Applied Mathematics
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In this manuscript we present a p-th degree immersed finite element method for solving boundary value problems with discontinuous coefficients. In this method, interface jump conditions are employed in the finite element basis functions, and the mesh does not have to be aligned with coefficient discontinuity. We show that under h refinement the immersed finite element solution converges to the true solution at the optimal O(h^p^+^1) and O(h^p) rates in the L^2 and H^1 norms, respectively. Furthermore, numerical results suggest that the immersed finite element solution converges exponentially fast under p refinement. Numerical examples are provided to illustrate features of this immersed finite element method.