Finite element solution of nonlinear elliptic problems
Numerische Mathematik
Nonlinear functional analysis and its applications
Nonlinear functional analysis and its applications
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
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Symmetric and Nonsymmetric Discontinuous Galerkin Methods for Reactive Transport in Porous Media
SIAM Journal on Numerical Analysis
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
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We develop a numerical method for the solution of convection-diffusion problems with a nonlinear convection and a quasilinear diffusion. We employ the so-called incomplete interior penalty Galerkin (IIPG) method which is suitable for a discretization of quasilinear diffusive terms. We analyse a use of the IIPG technique for a model scalar time-dependent convection-diffusion equation and derive hp a priori error estimates in the L^2-norm and the H^1-seminorm. Moreover, a set of numerical examples verifying the theoretical results is performed. Finally, we present a preliminary application of the IIPG method to the system of the compressible Navier-Stokes equations.