Displaying similar documents to “On the numerical solution of nonlinear partial differential equations on divergence form”

Analysis of the FEM and DGM for an elliptic problem with a nonlinear Newton boundary condition

Feistauer, Miloslav, Bartoš, Ondřej, Roskovec, Filip, Sändig, Anna-Margarete

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The paper is concerned with the numerical analysis of an elliptic equation in a polygon with a nonlinear Newton boundary condition, discretized by the finite element or discontinuous Galerkin methods. Using the monotone operator theory, it is possible to prove the existence and uniqueness of the exact weak solution and the approximate solution. The main attention is paid to the study of error estimates. To this end, the regularity of the weak solution is investigated and it is shown...

Newton's iteration with a conjugate gradient based decomposition method for an elliptic PDE with a nonlinear boundary condition

Jonas Koko (2004)

International Journal of Applied Mathematics and Computer Science

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Newton's iteration is studied for the numerical solution of an elliptic PDE with nonlinear boundary conditions. At each iteration of Newton's method, a conjugate gradient based decomposition method is applied to the matrix of the linearized system. The decomposition is such that all the remaining linear systems have the same constant matrix. Numerical results confirm the savings with respect to the computational cost, compared with the classical Newton method with factorization at each...

An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems

Xiao-Chuan Cai, Leszek Marcinkowski, Vassilevski, Panayot S. (2005)

Applications of Mathematics

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This paper extends previous results on nonlinear Schwarz preconditioning (Cai and Keyes 2002) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The nonlocal finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed...

Operator preconditioning with efficient applications for nonlinear elliptic problems

Janos Karátson (2012)

Open Mathematics

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This paper is devoted to the numerical solution of nonlinear elliptic partial differential equations. Such problems describe various phenomena in science. An approach that exploits Hilbert space theory in the numerical study of elliptic PDEs is the idea of preconditioning operators. In this survey paper we briefly summarize the main lines of this theory with various applications.