Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

Partial differential equations.

Mode of access: Internet.

Existence theorems in partial differential equations.

"Only the material on elliptic equations will appear in these notes."

Partial differential equations,

Mimeographed.

An implicit method for the solution of elliptic partial differential equations.

Supported in part by National Science Foundation under Grant No. U.S. NSF-GJ-328.

Singular solutions at boundary intersections in two dimensional quasi-linear homogeneous partial differential equations /

Includes bibliographical references (20).

Automatic solutions of partial differential equations.

Vita.

Notes on partial differential equations.

Cover title.

Partial differential equations : lecture notes, mathematics 365 /

Bibliography: leaf [77]

A Computer Algebra Application to Determination of Lie Symmetries of Partial Differential Equations

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Solutions of Analytical Systems of Partial Differential Equations

In this paper are examined some classes of linear and non-linear analytical systems of partial differential equations. Compatibility conditions are found and if they are satisfied, the solutions are given as functional series in a neighborhood of a given point (x = 0).

Hypoellipticity of Anisotropic Partial Differential Equations

2002 Mathematics Subject Classification: 35S05

Gevrey Local Solvability for Semilinear Partial Differential Equations

2002 Mathematics Subject Classification: 35S05

A posteriori error estimation for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations

We develop the a posteriori error estimation of interior penalty discontinuous Galerkin discretizations for H(curl)-elliptic problems that arise in eddy current models. Computable upper and lower bounds on the error measured in terms of a natural (mesh-dependent) energy norm are derived. The proposed a posteriori error estimator is validated by numerical experiments, illustrating its reliability and efficiency for a range of test problems.