High-resolution compact numerical method for the system of 2D quasi-linear elliptic boundary value problems and the solution of normal derivatives on an irrational domain with engineering applications
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DOI: 10.1007/s00366-020-01150-4
Abstract: In this paper, we present a novel approach to attain fourth-order approximate solution of 2D quasi-linear elliptic partial differential equation on an irrational domain. In this approach, we use nine grid points with dissimilar mesh… read more here.
Keywords: engineering; linear elliptic; solution normal; normal derivatives ... See more keywords
Expandable Parallel Finite Element Methods for Linear Elliptic Problems
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DOI: 10.1007/s10473-020-0218-2
Abstract: In this article, two kinds of expandable parallel finite element methods, based on two-grid discretizations, are given to solve the linear elliptic problems. Compared with the classical local and parallel finite element methods, there are… read more here.
Keywords: finite element; linear elliptic; parallel finite; expandable parallel ... See more keywords
Gradient estimates for semi-linear elliptic equations with prescribed contact angle problem
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DOI: 10.1016/j.jmaa.2017.05.066
Abstract: Abstract In this paper, we find a new auxiliary function and use the maximum principle to give a new proof for the gradient of a solution for semi-linear elliptic equations with capillarity-type problem. read more here.
Keywords: gradient estimates; linear elliptic; semi linear; elliptic equations ... See more keywords
Dirichlet problems for second order linear elliptic equations with $ L^{1} $-data
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DOI: 10.3934/cpaa.2023051
Abstract: We consider the Dirichlet problems for second order linear elliptic equations in non-divergence and divergence forms on a bounded domain $\Omega$ in $\mathbb{R}^n$, $n \ge 2$: $$ -\sum_{i,j=1}^n a^{ij}D_{ij} u + b \cdot D u… read more here.
Keywords: linear elliptic; elliptic equations; order linear; dirichlet problems ... See more keywords