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

SIAM Journal on Scientific Computing ◽

10.1137/140983537 ◽

2015 ◽

Vol 37 (4) ◽

pp. A1637-A1657 ◽

Author(s):

Mario Amrein ◽

Thomas P. Wihler

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Elliptic Partial Differential Equations ◽

Galerkin Methods ◽

Partial Differential ◽

Semilinear Elliptic ◽

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Adaptive pseudo-transient-continuation-Galerkin methods for semilinear elliptic partial differential equations

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22177 ◽

2017 ◽

Vol 33 (6) ◽

pp. 2005-2022 ◽

Author(s):

Mario Amrein ◽

Thomas P. Wihler

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Elliptic Partial Differential Equations ◽

Galerkin Methods ◽

Partial Differential ◽

Semilinear Elliptic

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Full Stability for a Class of Control Problems of Semilinear Elliptic Partial Differential Equations

SIAM Journal on Control and Optimization ◽

10.1137/17m1153224 ◽

2019 ◽

Vol 57 (4) ◽

pp. 3021-3045 ◽

Author(s):

Nguyen Thanh Qui ◽

Daniel Wachsmuth

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Elliptic Partial Differential Equations ◽

Control Problems ◽

Partial Differential ◽

Semilinear Elliptic

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Boundary-value problems for some semilinear elliptic partial differential equations

Coincidence Degree, and Nonlinear Differential Equations - Lecture Notes in Mathematics ◽

10.1007/bfb0089545 ◽

1977 ◽

pp. 151-165

Author(s):

Robert E. Gaines ◽

Jean L. Mawhin

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Boundary Value Problems ◽

Boundary Value ◽

Elliptic Partial Differential Equations ◽

Partial Differential ◽

Semilinear Elliptic

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Boundary Element Methods for Semilinear Elliptic Partial Differential Equations (II): Algorithms and Computations for Unstable Solutions from Various Models

Boundary Element Methods with Applications to Nonlinear Problems - Atlantis Studies in Mathematics for Engineering and Science ◽

10.2991/978-94-91216-27-5_12 ◽

2010 ◽

pp. 613-691

Author(s):

Goong Chen ◽

Goong Chen ◽

Jianxin Zhou

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Boundary Element ◽

Elliptic Partial Differential Equations ◽

Boundary Element Methods ◽

Partial Differential ◽

Semilinear Elliptic ◽

Unstable Solutions

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Boundary element monotone iteration scheme for semilinear elliptic partial differential equations

Mathematics of Computation ◽

10.1090/s0025-5718-96-00743-0 ◽

1996 ◽

Vol 65 (215) ◽

pp. 943-983 ◽

Author(s):

Yuanhua Deng ◽

Goong Chen ◽

Wei-Ming Ni ◽

Jianxin Zhou

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Boundary Element ◽

Elliptic Partial Differential Equations ◽

Iteration Scheme ◽

Partial Differential ◽

Monotone Iteration ◽

Semilinear Elliptic ◽

Monotone Iteration Scheme

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The Finite Element Approximation of Semilinear Elliptic Partial Differential Equations with Critical Exponents in the Cube

SIAM Journal on Scientific Computing ◽

10.1137/s1064827596312134 ◽

1999 ◽

Vol 20 (5) ◽

pp. 1875-1904 ◽

Author(s):

C. J. Budd ◽

A. R. Humphries ◽

A. J. Wathen

Keyword(s):

Finite Element ◽

Partial Differential Equations ◽

Differential Equations ◽

Critical Exponents ◽

Finite Element Approximation ◽

Elliptic Partial Differential Equations ◽

Element Approximation ◽

Partial Differential ◽

Semilinear Elliptic

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Adaptive fixed point iterations for semilinear elliptic partial differential equations

CALCOLO ◽

10.1007/s10092-019-0321-8 ◽

2019 ◽

Vol 56 (3) ◽

Author(s):

Mario Amrein

Keyword(s):

Fixed Point ◽

Partial Differential Equations ◽

Differential Equations ◽

Elliptic Partial Differential Equations ◽

Partial Differential ◽

Semilinear Elliptic ◽

Fixed Point Iterations

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Discontinuous Galerkin methods for elliptic partial differential equations with random coefficients

International Journal of Computer Mathematics ◽

10.1080/00207160.2013.784280 ◽

2013 ◽

Vol 90 (11) ◽

pp. 2477-2490 ◽

Author(s):

Kun Liu ◽

Béatrice M. Rivière

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Elliptic Partial Differential Equations ◽

Random Coefficients ◽

Galerkin Methods ◽

Partial Differential

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Boundary element monotone iteration scheme for semilinear elliptic partial differential equations, Part II: Quasimonotone iteration for coupled systems

Mathematics of Computation ◽

10.1090/s0025-5718-99-01109-6 ◽

1999 ◽

Vol 69 (230) ◽

pp. 629-653 ◽

Author(s):

Goong Chen ◽

Yuanhua Deng ◽

Wei-Ming Ni ◽

Jianxin Zhou

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Boundary Element ◽

Elliptic Partial Differential Equations ◽

Iteration Scheme ◽

Coupled Systems ◽

Partial Differential ◽

Monotone Iteration ◽

Semilinear Elliptic ◽

Monotone Iteration Scheme

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Some maximum principles for solutions of a class of partial differential equations inΩ⊂ℝn

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171200004877 ◽

2000 ◽

Vol 24 (11) ◽

pp. 749-751

Author(s):

Mohammad Mujalli Al-Mahameed

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Elliptic Partial Differential Equations ◽

Maximum Principles ◽

Partial Differential ◽

Semilinear Elliptic

We find maximum principles for solutions of semilinear elliptic partial differential equations of the forms: (1)Δ2u+αf(u)=0,α∈ℝ+and (2)ΔΔu+α(Δu)k+gu=0,α≤0in some regionΩ⊂ℝn.

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