Tag: Laplace equation
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MFEM Tutorials (1) Simplest MFEM of Laplace Problem
Description This example code demonstrates the most basic usage of MFEM to define a simple finite element discretization of the Laplace problem with zero Dirichlet boundary conditions. General 2D/3D mesh files and finite element polynomial degrees can be specified by command line options. Parse command line options This code includes the header files for the…
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Solving Partial Differential Equation by using Seperation of Variables : Part A. General Ways to Solve Laplace Equations
Here is another example of how to solve the Laplace equation for a simple rectangular domain using separation of variables, under the assumption of different boundary conditions: 1. Write the Laplace equation in the form: This is the general form of the Laplace equation, which holds for any rectangular domain. 2. Define the dimensions of…
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Partial Differential Equation (1) Laplace and Poisson Equation
From now, let’s talk about various partial differential equations. At first, I will talk about Laplace equation and Poisson equation. The Laplace equation is a second-order partial differential equation that arises in many physical systems, such as heat conduction, electrostatics, and fluid dynamics. It can be written in the following general form: where $u$ is…