Geodesic
Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type
Applications of Mathematics, Tome 41 (1996) no. 6, pp. 467-478

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A nonlinear elliptic partial differential equation with homogeneous Dirichlet boundary conditions is examined. The problem describes for instance a stationary heat conduction in nonlinear inhomogeneous and anisotropic media. For finite elements of degree $k\ge 1$ we prove the optimal rates of convergence $\mathcal O(h^k)$ in the $H^1$-norm and $\mathcal O(h^{k+1})$ in the $L^2$-norm provided the true solution is sufficiently smooth. Considerations are restricted to domains with polyhedral boundaries. Numerical integration is not taken into account.
A nonlinear elliptic partial differential equation with homogeneous Dirichlet boundary conditions is examined. The problem describes for instance a stationary heat conduction in nonlinear inhomogeneous and anisotropic media. For finite elements of degree $k\ge 1$ we prove the optimal rates of convergence $\mathcal O(h^k)$ in the $H^1$-norm and $\mathcal O(h^{k+1})$ in the $L^2$-norm provided the true solution is sufficiently smooth. Considerations are restricted to domains with polyhedral boundaries. Numerical integration is not taken into account.
DOI : 10.21136/AM.1996.134338
Classification : 35J65, 65N30, 74A15
Keywords: nonlinear boundary value problem; finite elements; rate of convergence; anisotropic heat conduction 
Liu, Liping; Křížek, Michal; Neittaanmäki, Pekka. Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type. Applications of Mathematics, Tome 41 (1996) no. 6, pp. 467-478. doi: 10.21136/AM.1996.134338
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